Question

If tan theta = √2 - 1 , prove that sin theta * cos theta = 1 / 2√ 2​.
Please don't use identity.
I will mark the answer as brainliest!

Answer 1

Answer:

done!!

Step-by-step explanation:

Answer 2

Step-by-step explanation:

theta is written as ' A '

tan A = √2 - 1

=> tan A = ( √2 - 1 ) / 1 = Perpendicular / Base

• Perpendicular = √2 - 1
• Base = 1

By Pythagoras theorem

=> ( Hypotenuse )² = ( Perpendicular )² + ( Base) ²

=> H² = ( √2 - 1 )² + 1²

=> H² = 2 + 1 - 2√2 + 1

=> H² = 4 - 2√2

=> H = √( 4 - 2√2 )

• sin A = Perpendicular / Hypotenuse = ( √2 - 1 ) / ( 4 - 2√2 )
• cos A = Base / Hypotenuse = 1 / ( 4 - 2√2 )

$\Rightarrow \sf sinA \times cosA = \dfrac{ \sqrt{2} - 1 }{ \sqrt{4 - 2 \sqrt{2} } } \times \dfrac{1}{ \sqrt{4 - 2 \sqrt{2} } } \\ \\ \\ \Rightarrow \sf sinA \times cosA = \dfrac{ \sqrt{2} - 1 }{4 - 2 \sqrt{2} } = \dfrac{ \sqrt{2} - 1 }{2 \sqrt{2} ( \sqrt{2} - 2) } = \dfrac{1}{2 \sqrt{2} }$

Hence proved.