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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