Question

Sin²α/1+cot²α+tan²α/(1+tan²α)²+cos²α=

Answer 1

Answer:

Step-by-step explanation:

sin²α/ (1+cot²α) + tan²α/(1+tan²α)² +cos²α

=sin²α/ cosec²α +  tan²α / sec⁴α +cos²α

=sin²α/(1/sin²α) + (sin²α/cos²α) / (1/cos⁴α)  + cos²α

=sin²α(sin²α) +(sin²α/cos²α)*cos⁴α + cos²α

=sun⁴α +sin²α*cos²α + cos²α

=sin²α( sin²α+cos²α) + cos²α

=sin²α *(1)+ cos²α

=sin²α + cos²α

=1

Thus 1 is correct answer