Prove that 2sin A/cos 3A + 2 sin3A/cos 9A +2sin9A/cos27A = tan 27A-tanA

2 sin A / cos 3A + 2 sin 3A / cos 9A + 2 sin 9A / cos 27A = tan 27A - tan A

2 sin A/cos 3A

Multiply with cos A to Numerator and denominator

= 2 sin A cos A/cos 3A cos A 

Formula (sin 2A = 2 sin A cos A)

= sin 2A / cos 3A cos A 

Formula [ (sin a-b) / cos a cos b = tan a - tan b ]

So, 

= sin 3A - A / cos 3A cos A

= tan 3A - tan A> Equation 1

Apply same procedure we get

2 sin3A / cos 9A = tan 9A - tan 3A---> Equation 2

2 sin 9A / cos 27A = tan 27A - tan 9A> Equation 3

Add Equation 1,2 and 3

tan 3A - tan A + tan 9A - tan 3A + tan 27A - tan 9A = tan 27A - tan A

2 sin A / cos 3A + 2 sin 3A / cos 9A + 2 sin 9A / cos 27A = tan 27A - tan A

Explanation:

hope this helps

can you list the selections

my biggest life lesson is that if you do something bad/wrong it comes straight back to you karma. one time this kid threw an snowball at me then he slipped on ice now that's karma.

explanation: