Question

(1−cosθ+sinθ)(1+cosθ+sinθ)=2sinθ(1−cos⁡θ+sin⁡θ)(1+cos⁡θ+sin⁡θ)=2sin⁡θ

• A. True
• B. False

Answer 1

The correct option is B False

$(1-\cos \theta +\sin \theta )(1+\cos \theta +\sin \theta )=(1+\sin \theta {)}^2-{\cos }^2\theta$

$=1+{\sin }^2\theta +2\sin \theta -{\cos }^2\theta$

$=(1-{\cos }^2\theta )+{\sin }^2\theta +2\sin \theta$

$=2\sin \theta +2{\sin }^2\theta$

So the given relation is $\text{False}$