Question

if sinx+cosx=1 then find the value of sin2x?

Answer 1

Answer:

sin 2x = 0.

Step-by-step explanation:

by squaring

sin x + cos x=1

sin square x + cos square x + 2cos x sin x

=2 sin x COS X.

(sin 2 x + cos 2 =1)

2 cos x sin x =0

and

sin 2x = 2 cos x sin x

SO

sin 2x = 0.

hope it helps u!!

Answer 2

Given:

A trigonometric equation sinx + cosx = 1.

To Find:

The value of Sin2x is?

Solution:

The given problem can be solved using trigonometric formulae.

1. The formulae used in solving the problem are:

• Sin²x + Cos²x = 1 ( Say Formula 1 )
• Sin2x = 2SinxCosx ( Say Formula 2 )

2. The given equation is Sinx + Cosx = 1,

=> Apply square on both the sides,

=> ( Sinx + Cosx )² = 1²,

=> Sin²x + Cos²x + 2SinxCosx = 1,

=> 1 + 2SinxCosx = 1, ( Formula 1 )

=> 2SinxCosx = 1 - 1,

=> 2SinxCosx = 0,

=> Sin2x = 0. ( Formula 2 )

Therefore, the value of sin2x is 0.