Results for Prove

How to Prove 1+cot^2(theta)=cosec^2(theta)

May 15, 2025

  



Use the Pythagorean identity:

sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1see how to prove it

Divide both sides of the identity by sin⁡2(θ)

sin⁡2(θ)sin⁡2(θ)+cos⁡2(θ)sin⁡2(θ)=1sin⁡2(θ) 

Final Answer:

1 + cot⁡2(θ)
=cosec⁡2(θ)

This proves the identity.



How to Prove tan^2(theta) +1=sec^2(theta)

May 15, 2025

 


Use the basic identity

sin⁡2(θ)+cos⁡2(θ)=1

\sin^2(\theta) + \cos^2(\theta) = 1

Divide both sides of the identity by cos⁡2(θ)\cos^2(\theta)

sin⁡2(θ)cos⁡2(θ)+cos⁡2(θ)cos⁡2(θ)=1cos⁡2(θ)\frac{\sin^2(\theta)}{\cos^2(\theta)} + \frac{\cos^2(\theta)}{\cos^2(\theta)} = \frac{1}{\cos^2(\theta)} tan⁡2(θ)+1=sec⁡2(θ)\tan^2(\theta) + 1 = \sec^2(\theta)

Final Answer:

tan⁡2(θ)+1=sec⁡2(θ)\boxed{\tan^2(\theta) + 1 = \sec^2(\theta)}

This proves the identity.




How to prove sin^2(theta)+cos^2(theta)=1

May 13, 2025




 fundamental trigonometric identity. It holds true for all values of

θ\theta, and it's one of the most important identities in trigonometry.

It comes directly from the Pythagorean Theorem applied to the unit circle. For any angle θ:




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