List of top Mathematics Questions on Trigonometric Identities

If \(A\) and \(B\) are the minimum and maximum values of \[ \sin^6 x+\cos^6 x, \] then \(A+B=\)
The value of \[ \sin^2 15^\circ+\cos^2 15^\circ \] is
Evaluate \[ 4\sin\frac{\pi}{6}\sin\frac{2\pi}{6}\sin\frac{3\pi}{6}\sin\frac{4\pi}{6}\sin\frac{5\pi}{6} \]
If \(x=\tan A, y=\tan B, z=\tan C\) and \[ xy+yz+zx=1, \] then evaluate \[ \frac{(1-x^2)(1-y^2)(1-z^2)}{(1+x^2)(1+y^2)(1+z^2)} \]
If \[ x=\sin18^\circ \] and \[ y=\tan22\frac12^\circ \] then \[ 4x(4x+2)= \]
If \[ \sin\theta+\cos\theta=1, \] then the value of \[ \sin\theta\cos\theta \] is:
If \[ \sin\theta+\cos\theta=\sqrt{2}\cos\alpha, \] where \(0<\theta<\frac{\pi}{2}\), then the value of \[ \sin2\theta \] is:
Evaluate \[ \frac{\cos\theta}{1-\cos\theta} + \frac{\sec\theta}{1+\sec\theta}. \]
If \(\alpha,\beta\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\), \[ \cos^4\alpha=\frac1{16},\qquad \sin^4\beta=\frac1{16} \] then \[ \cos\alpha+\cos\beta= \]
If \[ (\sin\theta+\cos\theta)^4+(\sin\theta-\cos\theta)^4 = p - q(\sin^4\theta+\cos^4\theta), \] then \(p+q=\)
If \(x+y = \frac{π}{4}\), then \((1+tanx)(1+tany) =\)
The value of \(cos15^{\circ}-sin15^{\circ}\) is ......
Let \(f_k(x) = \frac{1}{k}(cos^kx+sin^kx)\) where \(k\in N\), then \(f_6(x)-f_4(x) = \ldots\)
In \(△ABC\), if \(\angle C = \frac{π}{3}\), then the value of \(cos^2A+cos^2B+cosAcosB\) is...
The value of \(\frac{sin^23A}{sin^2A}-\frac{cos^23A}{cos^2A}\) is
If \(33θ = π\), then the value of \(cosθcos2θcos4θcos8θcos16θ\) is
If \(cos(θ-α) = a\) and \(sin(θ-β) = b\), then the value of \(cos^2(α-β)+2absin(α-β)+cos^2(θ-α)\) is...
\(tan105^{\circ} =\) ......
The value of \(cos^210^{\circ}-cos10^{\circ}cos50^{\circ}+cos^250^{\circ}\) is equal to....
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$
For an acute angle $\theta$, if $\sin \theta = \frac{1}{9}$, then value of $\frac{9\csc\theta + 1}{9\csc\theta - 1}$ is
Simplest form of $\frac{\sec A}{\sqrt{\sec^2 A - 1}}$ is
Prove that : $(1 + \cot \theta - \csc \theta)(1 + \tan \theta + \sec \theta) = 2$
Simplest form of $\frac{\sec A}{\sqrt{\sec^2 A - 1}}$ is
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$