How would you prove this identity?
sin²θ + tan²θ = sec²θ - cos²θ
These are the identities that i can use:
tanθ = sinθ / cosθ
cotθ = cosθ / sinθ
secθ = 1 / cosθ
cscθ = 1 / sinθ
sin²θ + cos²θ = 1
1 + cot²θ = csc²θ
1 + tan²θ = sec²θ
Thanks
sin²θ + tan²θ = sec²θ - cos²θ
These are the identities that i can use:
tanθ = sinθ / cosθ
cotθ = cosθ / sinθ
secθ = 1 / cosθ
cscθ = 1 / sinθ
sin²θ + cos²θ = 1
1 + cot²θ = csc²θ
1 + tan²θ = sec²θ
Thanks
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RHS = sec^2 A -- cos^2 A
= 1 + tan^2 A -- (1 -- sin^2 A)
= 1 + tan^2 A -- 1 + sin^2 A
= sin^2 A + tan^2 A
= LHS
= 1 + tan^2 A -- (1 -- sin^2 A)
= 1 + tan^2 A -- 1 + sin^2 A
= sin^2 A + tan^2 A
= LHS