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Range of Trigonometric Ratios from 0 to 90 Degrees

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Question

What is the value of (1 + tan² θ) (1 − sin θ) (1 + sin θ)?

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Solution

We have,

We know that,

Therefore,

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(1 + {tan}^{2} θ) (1 - sin θ) (1 + sin θ)

(1 + {tan}^{2} θ) (1 + sin θ) (1 - sin θ)

(1 + {tan}^{2} θ) (1 + sin θ) (1 - sin θ) = 1

Q. Question 11
Simplify:

(1 + t a n^{2} θ) (1 - s i n θ) (1 + s i n θ)

Q. Prove the following trigonometric identities.

(1 + tan²θ) (1 − sinθ) (1 + sinθ) = 1

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Range of Trigonometric Ratios from 0 to 90 Degrees

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