Introduction to Trigonometry — Class 10 Mathematics (Standard) PYQs

For an acute angle $\theta$, if $\cos \theta =\frac{1}{8}$, then $\frac{8\sec \theta +1}{8\sec \theta -1}$ equals

Simplest form of $\frac{\sec A}{\sqrt{{\sec }^{2}A-1}}$ is

(a) For acute angles $A$ and $B$, if $\sec (2A-B)=\sqrt{2}$ and $\csc (A+B)=2$, then find the values of $A$ and $B$.
OR
(b) Evaluate : $\frac{2\cos 30^{\circ }-{\cot }^{3}60^{\circ }}{\tan 30^{\circ }}$

Prove that : $(1+\cot \theta -\csc \theta )(1+\tan \theta +\sec \theta )=2$

For an acute angle $\theta$, if $\sin \theta =\frac{1}{9}$, then value of $\frac{9\csc \theta +1}{9\csc \theta -1}$ is

(a) Evaluate : $\frac{{\sin }^{3}60^{\circ }-\tan 30^{\circ }}{{\cos }^{2}45^{\circ }}$
OR
(b) For acute angles $A$ and $B$ and $A + 2B$ and $2A + B$ are acute if $\tan (A+2B)=\sqrt{3}$ and $\sin (2A+B)=\frac{1}{\sqrt{2}}$, then find the measures of angles $A$ and $B$.

Prove that : $\frac{\tan \theta }{1-\cot \theta }+\frac{\cot \theta }{1-\tan \theta }=1+\tan \theta +\cot \theta$

If $\theta$ is an acute angle and $7+4\sin \theta =9$, then the value of $\theta$ is :

The value of ${\tan }^2\theta -\frac{1}{\cos \theta \cdot \sec \theta }$ is :

(a) If $x\cos 60^{\circ }+y\cos 0^{\circ }+\sin 30^{\circ }\cot 45^{\circ }=5$, then find the value of $x + 2y$.
OR
(b) Evaluate : $\frac{{\tan }^{2}60^{\circ }}{{\sin }^{2}60^{\circ }+{\cos }^{2}30^{\circ }}$