Trigonometry
Prove the following identities:
1. (tan theta  sin theta)^2 + (1cos theta)^2 = (1sec theta) ^2
2. (12cos^2 theta) / sin theta cos theta = tan theta  cot theta
3. (sin theta + cos theta ) ^2 + (sin theta  cos theta ) ^2 = 2
Thank you so much! :)
asked by
Fern Angel

sinθ = tanθ cosθ, so
tanθ  sinθ = tanθ (1cosθ)
squared that is tan^2θ (1cosθ)^2
now we can add up the left side:
tan^2θ(1cosθ)^2 + (1cosθ)^2
= (tan^2θ + 1)(1cosθ)^2
= sec^2θ (1cosθ)^2
on the right side, we have
1secθ = (cosθ1)/cosθ
squared, that is sec^2θ (cosθ1)^2
and they are the sameposted by Steve
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