Question

Soleve this math problem​

Answer 1

Answer:

Hence proved.

Step-by-step explanation:

The expression is $sin^{4}\alpha +cos^{4}\alpha +1=2sin^{2}\alpha$

Solve the expression as follows:

$sin^{4}\alpha -cos^{4}\alpha +1=(sin^{2}\alpha)^{2} -(cos^{2}\alpha)^{2} +1$

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

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

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

                             $=sin^{2}\alpha +sin^{2}\alpha -1+1$

                             $=2sin^{2}\alpha$

Hence proved.