Question

If A =30 and B =60. verifiy that 2 sin A cosA =2tanA/1+tan²A​

Answer 1

Explanation:

It's given that A = 30° . Lets find the sin , cos & tan of A

⇒
`\sin A=\sin30 = (1)/(2)`

⇒
`\cos A = \cos 30 = (√(3) )/(2)`

⇒
`\tan A = \tan 30 = (1)/(√(3) )`

Lets solve the LHS (Left Hand Side) :-

`2(\sin A * \cos A) = 2((1)/(2) * (√(3) )/(2)) = (√(3) )/(2)`

Now lets solve the RHS (Right Hand Side) :-

`(2\tan A)/(1+\tan ^(2)A ) = (2 * (1)/(√(3) ) )/(1 + ((1)/(√(3) ) )^(2) ) = (2)/(√(3) ) / ( 1 + (1)/(3) ) = (2)/(√(3) )/ (4)/(3) = (2)/(√(3) ) *(3)/(4) =(√(3) )/(2)`

∴ LHS = RHS ( Proved )