Question

prove that
cos2A-cos12A/sin12A-sin2A=tan7A
​

Answer 1

Step-by-step explanation:

cosA - CosB = 2sin( A +B )/2 sin ( B - A )/2

SinA - Sin B = 2cos ( A + B )/2 sin ( A - B )/2

Now put the given values in these formulas

LHS

= 2sin( 2A + 12A )/2 sin( 12A - 2A )/2 / 2cos ( 12A + 2A ) sin 12A - 2A )/2

= 2sin7A sin5A / 2cos7A sin5A

= sin5A will cancel out

= therefore the remaining part will be 2 sin7A/ 2cos7A

= > 2sin7A/ 2cos7A = tan7A

Hence proved...