What is the value of $\cos^4\frac{7\pi}{8}+\cos^4\frac{5\pi}{8}?$

What is $\sin^2\left(\frac{\pi}{4}+\theta\right)-\sin^2\left(\frac{\pi}{4}-\theta\right)$ equal to?

If tan α + tan β = 1 - tan α.tan β, where tan α tan β ≠ 1, then which of the following is one of the values of (α + β) ?

If (1 + tan θ) (1 + tan 9θ) = 2, then what is the value of tan(10θ)?