Question

prove that cos² ( 1 + tan² ) = 1​

Answer 1

Heya mate! Here's your Answer!

cos²(1 + tan²)

cos²(1 + $\frac{sin^{2} }{cos^2}$)                                                    (tan² = $\frac{sin^{2} }{cos^2}$)

cos² + cos² x $\frac{sin^{2} }{cos^2}$                                            (canceling cos²)

cos² + sin²                                                       (cos² + sin² = 1)

=1

Hence, proved that cos²(1 + tan²) = 1

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Answer 2

Answer:

TO PROVE,

Step-by-step explanation: Let , cos²(1+tan²) be equation 1

w.k.t , 1+tan²θ=sec²θ

substitute value of 1+tan²θ in equation 1

cos²θ(sec²θ)=

according to identity ,  cos²θ*sec²θ=1

cos²θ(sec²θ)=1.

HENCE PROVED