Simplify (1 + tan² θ) (1 - sinθ) (1 + sinθ)

Solution:

It is given that

(1 + tan² θ) (1 - sinθ) (1 + sinθ)

As 1 + tan² θ = sec² θ

So we can write it as

= sec² θ (1 - sinθ) (1 + sinθ)

Using the algebraic identity

a² - b² = (a + b) (a - b)

We get

= sec² θ (1 - sin² θ)

We know that

1 - sin² θ = cos² θ

By substituting it

= sec² θ cos² θ

Here cos² θ = 1/sec² θ

So we get

= sec² θ . 1/sec² θ

= 1

Therefore, by simplification we get 1.

✦ Try This: The value of sec (90° - θ) sin θ is a. sec θ, b. cosec θ, c. tan θ, d. 1

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8

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NCERT Exemplar Class 10 Maths Exercise 8.3 Problem 11

Simplify (1 + tan² θ) (1 - sinθ) (1 + sinθ)

Summary:

There are 6 basic trigonometric ratios used in trigonometry, also called trigonometric functions- sine, cosine, secant, cosecant, tangent, and cotangent, written as sin, cos, sec, csc, tan, cot in short. By simplification of (1 + tan² θ) (1 - sinθ) (1 + sinθ), we get 1

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