Question

prove that (1+sinA)²+(1-sinA)²/cos²Α=2(1+sin²Α/1-sin²Α)

Answer 1

Answer on Question #69292 – Math – Trigonometry

Question

Prove that

$$\frac{(1 + \sin A)^2 + (1 - \sin A)^2}{(\cos A)^2} = 2 \frac{1 + (\sin A)^2}{1 - (\sin A)^2}$$

Solution

$$\frac{(1 + \sin A)^2 + (1 - \sin A)^2}{(\cos A)^2} = \frac{1 + 2 \sin A + (\sin A)^2 + 1 - 2 \sin A + (\sin A)^2}{(\cos A)^2} = \frac{2 + 2 (\sin A)^2}{(\cos A)^2} = 2 \frac{1 + (\sin A)^2}{1 - (\sin A)^2}.$$

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