Question

Show 1- tan square a by 1+tan square a = 2 cos square a-1

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

The given equation is $\frac{(1-tan^{2}a)}{(1+tan^{2}a)}=2cos^{2}a-1$

We take the left hand side of the equation,

$\frac{(1-tan^{2}a)}{(1+tan^{2}a)}$=$\frac{(1-\frac{sina^{2}a}{cos^{2}a}}{(1+\frac{sin^{2}a}{cos^{2}a})}$

            = $\frac{\frac{cos^{2}a-sin^{2}a}{cos^{2}a}}{\frac{sin^{2}a+cos^{2}a}{cos^{2}a}}$

            = $\frac{cos^{2}a-sin^{2}a}{sin^{2}a+cos^{2}a}$

            = $\frac{cos^{2}a-(1-cos^{2}a)}{1}$

            = $2cos^{2}a-1$

            = Right hand side of the equation.

Hence proved.

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