Question

Find this guyz trig.....

Answer 1

Given Equation is cot(A + 15) - tan(A - 15)

It can be written as,

= > [cos(A + 15)/sin(A + 15)] - [(sin(A - 15)/cos(A - 15))]

= > [cos(A + 15)cos(A - 15) - sin(A - 15)sin(A + 15)]/sin(A + 15)cos(A - 15) ---- (1)

We know that cosAcosB - sinAsinB = cos(A + B)

= > cos(A + 15 + A - 15)

= > cos 2A.

Now,

Equation (1) can be written as,

= > cos2A/sin(A + 15)cos(A - 15)

Multiply the numerator and denominator with '2', we get

= > 2cos2A/2sin(A + 15)cos(A - 15) ------- (2)

We know that 2sinAcosB = sin(A + B) + sin(A - B)

$= > \frac{2cos2A}{sin2A + sin30}$

$= > \frac{2cos2A}{sin2A + \frac{1}{2}}$

$= > \frac{2cos2A}{(\frac{sin2A + 1)}{2}}$

$= > \frac{4cos2A}{sin2A + 1}$

Hope this helps!