In a triangle prove that sin 2 </msup> &#x2061;<!-- ⁡ --> ( <mrow class="

Wronsonia8g

Wronsonia8g

Answered question

2022-07-09

In a triangle prove that sin 2 ( A 2 ) + sin 2 ( B 2 ) + sin 2 ( C 2 ) + 2 sin ( A 2 ) sin ( B 2 ) sin ( C 2 ) = 1

Answer & Explanation

diamondogsaz

diamondogsaz

Beginner2022-07-10Added 12 answers

Let x = A 2 , y = B 2 , z = C 2 , x + y + z = π / 2
sin 2 ( x ) + sin 2 ( y ) + sin 2 ( z ) + 2 sin ( x ) sin ( y ) sin ( z ) = sin 2 ( x ) + sin 2 ( y ) + sin 2 ( π / 2 x y ) + 2 sin ( x ) sin ( y ) sin ( π / 2 x y ) = sin 2 ( x ) + sin 2 ( y ) + cos 2 ( x + y ) + 2 sin ( x ) sin ( y ) cos ( x + y ) = sin 2 ( x ) + sin 2 ( y ) + cos 2 ( x + y ) + ( cos ( x y ) cos ( x + y ) ) cos ( x + y ) = sin 2 ( x ) + sin 2 ( y ) + cos ( x y ) cos ( x + y ) = 1 cos ( 2 x ) 2 + 1 cos ( 2 y ) 2 + cos ( x y ) cos ( x + y ) = 1 cos ( 2 x ) + cos ( 2 y ) 2 + cos ( x y ) cos ( x + y ) = 1 cos ( x y ) cos ( x + y ) + cos ( x y ) cos ( x + y ) = 1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?