Getting Rid of the Angle α

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Introduction to Trigonometry

Getting Rid of the Angle α

CBSE Class 10 · Solve it one decision at a time. A wrong pick earns a nudge, never the answer.

Step 1 of 4

The problem

If tan⁡θ=ntan⁡α\tan\theta = n\tan\alpha and sin⁡θ=msin⁡α,\sin\theta = m\sin\alpha, prove that cos⁡2θ=m2−1n2−1.\cos^2\theta = \dfrac{m^2 - 1}{n^2 - 1}.

Step 1 · Your move

Divide sin⁡θ=msin⁡α\sin\theta = m\sin\alpha by tan⁡θ=ntan⁡α\tan\theta = n\tan\alpha. What is cos⁡θ\cos\theta?

tan⁡θ=ntan⁡α,sin⁡θ=msin⁡α\tan\theta = n\tan\alpha,\quad \sin\theta = m\sin\alpha
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