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Integration by Substitution

Solve: sin90...

Question

Solve: $\frac{sin (90^{o} + A)}{cos (- A)} - \frac{sin (180^{o} - A)}{sin (- A)} + \frac{tan (270^{o} + A)}{cot (- A)} = 3$

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Solution

$L . H . S = \frac{sin (90^{o} + A)}{cos (- A)} - \frac{sin (180^{o} - A)}{sin (- A)} + \frac{tan (270^{o} + A)}{cot (- A)} = \frac{cos A}{cos A} - \frac{sin A}{(- sin A)} + \frac{(- cot A)}{(- cot A)} = \frac{cos A}{cos A} + \frac{sin A}{sin A} + \frac{cot A}{cot A} = 3 = R . H . S$

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