Skip to main content
Yukti Vault

Trigonometry

Trigonometric Ratio & Identities: JEE Main & Advanced PYQs

381 previous year questions on Trigonometric Ratio & Identities from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

Practice this chapter

Questions 351-381 of 381

  1. In a $\Delta PQR$, if $3\sin P+4\cos Q=6$ and $4\sin Q+3\cos P=1$, then the angle $R$ is equal to :
  2. Consider the following statements connecting a triangle $ABC$: (i) The sides $a,b,c$ and area $\Delta$ are rational. (ii) $a,\tan\dfrac{B}{2},\tan\dfrac{C}{2}$ are …
  3. The number of solutions of the equation $|\cos x|=\cos x-2\sin x$, $-2\pi\le x\le2\pi$, is
  4. The number of roots of the equation, $(81)^{\sin^{2}x}+(81)^{\cos^{2}x}=30$ in the interval $[0,\pi]$ is equal to :
  5. If for $x\in\left(0,\dfrac{\pi}{2}\right)$, $\log_{10}\sin x+\log_{10}\cos x=-1$ and $\log_{10}(\sin x+\cos x)=\dfrac{1}{2}\left(\log_{10}n-1\right)$, $n>0$, then the …
  6. Suppose $\theta\in\left[0,\dfrac{\pi}{4}\right]$ is a solution of $4\cos\theta-3\sin\theta=1$. Then $\cos\theta$ is equal to :
  7. The number of solutions of $\sin^{2}x+\left(2+2x-x^{2}\right)\sin x-3(x-1)^{2}=0$, where $-\pi\le x\le\pi$, is $\_\_\_\_\_\_\_\_$ .
  8. If $L=\sin^{2}\left(\dfrac{\pi}{16}\right)-\sin^{2}\left(\dfrac{\pi}{8}\right)$ and $M=\cos^{2}\left(\dfrac{\pi}{16}\right)-\sin^{2}\left(\dfrac{\pi}{8}\right)$, then :
  9. The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be $45^{\circ}$. After walking a …
  10. The sum of all values of $\theta\in[0,2\pi]$ satisfying $2\sin^{2}\theta=\cos2\theta$ and $2\cos^{2}\theta=3\sin\theta$ is
  11. The value of $\left(\sin70^{\circ}\right)\left(\cot10^{\circ}\cot70^{\circ}-1\right)$ is
  12. Let $A=\left\{x\in(0,\pi)-\left\{\dfrac{\pi}{2}\right\}:\log_{(2/\pi)}|\sin x|+\log_{(2/\pi)}|\cos x|=2\right\}$ and …
  13. If …
  14. In a triangle with sides $a,b,c$, if $r_1>r_2>r_3$ (which are the ex-radii) then :
  15. The sides of a triangle are $3x+4y$, $4x+3y$ and $5x+5y$ where $x,y>0$, then the triangle is :
  16. The sum of the radii of inscribed and circumscribed circles for an $n$ sided regular polygon of side $a$, is :
  17. If in a $\triangle ABC$, $a\cos^{2}\left(\frac C2\right)+c\cos^{2}\left(\frac A2\right)=\frac{3b}{2}$, then the sides $a,b$ and $c$ :
  18. In a triangle $ABC$, medians $AD$ and $BE$ are drawn. If $AD=4$, $\angle DAB=\frac{\pi}{6}$ and $\angle ABE=\frac{\pi}{3}$, then the area of the $\triangle ABC$ is :
  19. A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is $60^\circ$ and when he retires …
  20. The sides of a triangle are $\sin\alpha$, $\cos\alpha$ and $\sqrt{1+\sin\alpha\cos\alpha}$ for some $0<\alpha<\frac{\pi}{2}$. Then the greatest angle of the triangle is :
  21. In a triangle $ABC$, let $\angle C=\frac{\pi}{2}$. If $r$ is the inradius and $R$ is the circumradius of the triangle $ABC$, then $2(r+R)$ equals :
  22. If in a $\triangle ABC$, the altitudes from the vertices $A,B,C$ on opposite sides are in H.P., then $\sin A,\sin B,\sin C$ are in :
  23. The number of values of $x$ in the interval $[0,3\pi]$ satisfying the equation $2\sin^{2}x+5\sin x-3=0$ is
  24. A tower stands at the centre of a circular park. $A$ and $B$ are two points on the boundary of the park such that $AB\,(=a)$ subtends an angle of $60^\circ$ at the foot …
  25. $AB$ is a vertical pole with $B$ at the ground level and $A$ at the top. A man finds that the angle of elevation of the point $A$ from a certain point $C$ on the ground …
  26. For a regular polygon, let $r$ and $R$ be the radii of the inscribed and the circumscribed circles. A false statement among the following is :
  27. If the angles of elevation of the top of a tower from three collinear points $A$, $B$ and $C$, on a line leading to the foot of the tower, are $30^\circ$, $45^\circ$ and …
  28. A bird is sitting on the top of a vertical pole $20$ m high and its elevation from a point $O$ on the ground is $45^\circ$. It flies off horizontally straight away from …
  29. $ABCD$ is a trapezium such that $AB$ and $CD$ are parallel and $BC\perp CD$. If $\angle ADB=\theta$, $BC=p$ and $CD=q$, then $AB$ is equal to:
  30. The number of solutions of $\tan x+\sec x=2\cos x$ in $[0,2\pi]$ is
  31. Let in a right angled triangle, the smallest angle be $\theta$. If a triangle formed by taking the reciprocal of its sides is also a right angled triangle, then …

Other chapters