Question

Prove that -- this trigonometry equation.
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Answer 1

We know that,

sin(90°+∅) = cos∅

sin(180°+∅) = -sin∅

tan(90°+∅) = -cot∅

sin(-∅) = -sin∅

Now,

$\frac{sin(90 + A)}{cosA} + \frac{ sin( - A)}{sin(180 + A)} - \frac{tan(90 + A)}{cotA} \\ = \frac{cosA}{cosA} + \frac{ - sinA}{ - sinA} - \frac{cotA}{cotA} \\ = 1 + 1 + 1 = 3$