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GREYUIT [131]
3 years ago
10

How to do question 27

Mathematics
1 answer:
GenaCL600 [577]3 years ago
5 0
1/(sin(90 + θ)cos(360 - θ))     -   tan²(-θ)

Note:

 sin(90 + θ) = cosθ        Cosine and Sine are complementary.

cos(360 - θ) = cosθ      Cosine positive in 4th quadrant.

tan(-θ) = -tanθ          Negative angle concept.


1/(sin(90 + θ)cos(360 - θ))     -   tan²(-θ) =  1/(cosθcosθ)     -   (-tanθ)²

                                                                 =  1/(cos²θ)     -       tan²θ

                                                                  =  (1/cosθ)²     -       tan²θ
Note: 1/cosθ = secθ

                                                                 =  (secθ)²     -       tan²θ

                                                                  =  sec²θ     -       tan²θ

                                                                  =  1


Note that    1+ tan²θ = sec²θ is a Trigonometric identity.

That means:  sec²θ     -       tan²θ = 1

Hope this explains it.
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