Question

If a=60,verify that
$1) \sin(2a) = \frac{2 \tan(a) }{1 + { \tan }^{2} a} \\ 2) \tan(2a) = \frac{2 \tan(a) }{1 - { \tan }^{2}a }$

Answer 1

Hey !!

sin2A = 2sinA×cosA /1

we can write 1 as denominator ..

=> 2sinA×cosA /cos²A + sin²A
(•°• sin²A + cos²A = 1)

=> 2sinA×cosA/cos²A
--------------------------------
cos²A + cos²A /cos²A

=> 2 tanA /1 + tan²A RHS prooved


Q2nd ..

•°• tan(A + B ) = tanA + tanB/1 - tanA ×tanB

similarly

tan2A = tan(A+A)

= tanA + tanA /1 - tanA×tanA

= 2tanA/1-tan²A prooved

LHS = RHS


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Hope it helps !!.

@Rajukumar111