Educational

If α + β = π/4, Find the Value of (1 + tan α)(1 + tan β) If α + β = π/4, Find the Value of (1 + tan α)(1 + tan β) Question: If \[ \alpha+\beta=\frac{\pi}{4} \] then the value of \[ (1+\tan\alpha)(1+\tan\beta) \] is (a) \(1\) (b) \(2\) (c) \(-2\) (d) not […]

If tan 69° + tan 66° − tan 69° tan 66° = 2k, Find k If tan 69° + tan 66° − tan 69° tan 66° = 2k, Find k Question: If \[ \tan69^\circ+\tan66^\circ-\tan69^\circ\tan66^\circ=2k \] then \[ k= \] (a) \(-1\) (b) \(\frac{1}{2}\) (c) \(-\frac{1}{2}\) (d) none of these Solution Using the identity: \[ \tan(A+B)

If cos(A − B) = 3/5 and tan A tan B = 2, Find cos A cos B and sin A sin B If cos(A − B) = 3/5 and tan A tan B = 2, Find cos A cos B and sin A sin B Question: If \[ \cos(A-B)=\frac{3}{5} \] and \[ \tan A\tan

Find the Maximum Value of sin²(2π/3 + x) + sin²(2π/3 − x) Find the Maximum Value of sin²(2π/3 + x) + sin²(2π/3 − x) Question: The maximum value of \[ \sin^2\left(\frac{2\pi}{3}+x\right) + \sin^2\left(\frac{2\pi}{3}-x\right) \] is (a) \(\frac{1}{2}\) (b) \(\frac{3}{2}\) (c) \(\frac{1}{4}\) (d) \(\frac{3}{4}\) Solution Use the identity: \[ \sin^2\theta=\frac{1-\cos2\theta}{2} \] Therefore, \[ \sin^2\left(\frac{2\pi}{3}+x\right) = \frac{

If A − B = π/4, Find (1 + tan A)(1 − tan B) If A − B = π/4, Find (1 + tan A)(1 − tan B) Question: If \[ A-B=\frac{\pi}{4} \] then \[ (1+\tan A)(1-\tan B) \] is equal to (a) \(2\) (b) \(1\) (c) \(0\) (d) \(3\) Solution Using the identity: \[

If tan(A − B) = 1 and sec(A + B) = 2/√3, Find the Smallest Positive Value of B If tan(A − B) = 1 and sec(A + B) = 2/√3, Find the Smallest Positive Value of B Question: If \[ \tan(A-B)=1 \] and \[ \sec(A+B)=\frac{2}{\sqrt3} \] then the smallest positive value of \[ B

If tan(π/4 + x) + tan(π/4 − x) = a, Find tan²(π/4 + x) + tan²(π/4 − x) If tan(π/4 + x) + tan(π/4 − x) = a, Find tan²(π/4 + x) + tan²(π/4 − x) Question: If \[ \tan\left(\frac{\pi}{4}+x\right) + \tan\left(\frac{\pi}{4}-x\right) =a \] then \[ \tan^2\left(\frac{\pi}{4}+x\right) + \tan^2\left(\frac{\pi}{4}-x\right) = \] (a) \(a^2+1\) (b) \(a^2+2\)

Find the Value of cos(36° − A) cos(36° + A) + cos(54° + A) cos(54° − A) Find the Value of cos(36° − A) cos(36° + A) + cos(54° + A) cos(54° − A) Question: The value of \[ \cos(36^\circ-A)\cos(36^\circ+A) + \cos(54^\circ+A)\cos(54^\circ-A) \] is (a) \(\sin2A\) (b) \(\cos2A\) (c) \(\cos3A\) (d) \(\sin3A\) Solution Using the

If tan θ = 1/2 and tan ϕ = 1/3, Find the Value of θ + ϕ If tan θ = 1/2 and tan ϕ = 1/3, Find the Value of θ + ϕ Question: If \[ \tan\theta=\frac{1}{2} \] and \[ \tan\phi=\frac{1}{3} \] then the value of \[ \theta+\phi \] is (a) \(\frac{\pi}{6}\) (b) \(\pi\)

If sin(π cos x) = cos(π sin x), Find sin 2x If sin(π cos x) = cos(π sin x), Find sin 2x Question: If \[ \sin(\pi\cos x)=\cos(\pi\sin x) \] then \[ \sin2x= \] (a) \(\pm\frac{3}{4}\) (b) \(\pm\frac{4}{3}\) (c) \(\pm\frac{1}{3}\) (d) none of these Solution Using the identity: \[ \cos\theta=\sin\left(\frac{\pi}{2}-\theta\right) \] Therefore, \[ \sin(\pi\cos x) =