91Ó°ÊÓ

Solve the following equations and tick the correct one. 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 (a) 6 (b) 1 (c) 2 (d) 4

If \(A\) and \(B\) are acute \(+\) ve angles satisfying the equations \(3 \sin ^{2} A+2 \sin ^{2} B=1\) and \(3 \sin 2 A=2 \sin 2 B\), then find \((A+2 B)\).

Solve the following trigonometric equations: Find the number of integral ordered pairs satisfy the equations \(\left\\{\begin{array}{l}\cos (x y)=x \\ \tan (x y)=y\end{array}\right.\)

Solve the following equations and tick the correct one. The number of values of \(x\) in \([0,5 \pi]\) satisfying the equation \(3 \sin ^{2} x-7 \sin x+2=0\) is (a) 0 (b) 5 (c) 6 (d) 10

Solve the following equations and tick the correct one. The number of solution of the equation \(|\cot x|=\cot x+\frac{1}{\sin x}, 0

Solve the following trigonometric equations: Find the number of real solutions of \(\sin ^{2016} x-\cos ^{2016} x=1\) in \([0,2 \pi]\)

If \(\tan (A-B)=1\) and \(\sec (A+B)=\frac{2}{\sqrt{3}}\), then find the smallest +ve values of \(A\) and \(B\) and their most general values.

If \(\sin A=\sin B\) and \(\cos A=\cos B\), then find the values of \(A\) in terms of \(B\).

Solve the following equations and tick the correct one. The number of solution of \(|\cos x|=\sin x\) such that \(0

Solve the following trigonometric equations: Find the number of ordered pairs which satisfy the equation \(x^{2}+2 x \sin (x y)+1=0\) for \(y \in[0,2 \pi]\).