Question

This is worth 100 points so be serious Prove this: tan^2 A+ cot^2 A+2= sec^2 A . Cosec^2 A

Answer 1

Answer:

to prove : cot2A−cot2B=cos2A−cos2Bsin2A∗sin2B=cosec2A−cosec2B

Step-by-step explanation:

to proove : cot2A−cot2B=cosec2A−cosec2B

LHS : cot2A−cot2B

=(cosec2A−1)−(cosec2B−1)

=cosec2A−1−cosec2B+1

=cosec2A−cosec2B: RHS

Now the other one:

cot2A−cot2B=cos2A−cos2Bsin2A∗sin2B

LHS : cot2A−cot2B

=cosec2A−cosec2B {PROVED ABOVE}

=1sin2A−1sin2B

=sin2B−sin2Asin2A∗sin2B

=(1−cos2B)−(1−cos2A)sin2A∗sin2B

=1−cos2B−1+cos2Asin2A∗sin2B

=cos2A−cos2Bsin2A∗sin2B: RHS

please mark brainliestt dear ❣️❣️❣️❣️

Answer 2

Answer:

=tan^2+cot^2+2tanA.cotA

=tan^2+cot^2+2

=(tan^2+1)+(cot^2+1)

=cosec^2A+sec^2A

Q.E.D.