Prove that:(tan5φ+tan3φ)/(tan5φ-tan3φ)=4cos2φcos4φ?

Question

pls show me the method.......wnt 2 get ans by 2moro morning...

Answer 1

We start with:

(tan (5φ) + tan (3φ))/(tan (5φ) - tan (3φ))

Multiply both the numerator and denominator by cos (3φ) cos (5φ):

(sin (5φ) cos (3φ) + sin (3φ) cos (5φ))/(sin (5φ) cos (3φ) - sin (3φ) cos (3φ))

Using the angle addition formula for sine:

sin (5φ+3φ)/sin (5φ-3φ)

Simplify:

sin (8φ)/sin (2φ)

Expanding the numerator using the double angle formula:

2 sin (4φ) cos (4φ)/sin (2φ)

Expand the sin (4φ) using the double angle formula:

4 sin (2φ) cos (2φ) cos (4φ)/sin (2φ)

Cancel the sin (2φ):

4 cos (2φ) cos (4φ)

And we are done.

Answer 2

Honey, you need to re-write the problem. It didn't show up. It cuts off after tan3...