Question 109

If $$\cos^2 \theta - \sin^2 \theta = \tan^2 \phi$$ then which of the following is true?

Solution

Expression : $$\cos^2 \theta - \sin^2 \theta = \tan^2 \phi$$

=> $$cos^2\theta-sin^2\theta=\frac{sin^2\phi}{cos^2\phi}$$

=> $$\frac{cos^2\theta-sin^2\theta}{cos^2\theta+sin^2\theta}=\frac{sin^2\phi}{cos^2\phi}$$

By componendo and dividendo

=> $$\frac{-sin^2\theta}{cos^2\theta}=\frac{sin^2\phi-cos^2\phi}{sin^2\phi+cos^2\phi}$$

=> $$cos^2\phi-sin^2\phi=tan^2\theta$$

=> Ans - (B)

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