Question

(ii) (1 + tan? A) (1 + sin A) (1 - sin A) = 1​

Answer 1

Answer:

Proved

Step-by-step explanation:

We have to prove (1 + tan²A) (1 + sin A) (1 - sin A) = 1

Solve LHS term:

• (1 + tan²A) (1 + sin A) (1 - sin A)

→ ( 1 + tan² A) ( 1 - Sin²A)

→ Sec²A × Cos²A

→ SEC²A × 1/Sec²A

→ Cancel sec²A

→ 1

Important Trigonometry Identities:

• 1 + tan² A = Sec²A
• 1/Cos²A = Sec²A
• Sin²A + Cos²A = 1

Answer 2

Answer:

(1 + tan² A) (1 + sin A) (1 - sin A) = 1

Hence, L.H.S. = R.H.S.

Step-by-step explanation:

L.H.S. = (1 + tan² A) (1 + sin A) (1 - sin A)

L.H.S. = (1 + tan² A) (1 - sin² A)

L.H.S. = sec²A × 1/sec²A

[°.° 1 + tan² A = sec²A]

sec²A is cancelled because sec²A is as like as numerator and 1/sec²A is as like as denominator.

When denominator and numerator contains same value, it is divided with 1 which is cancelled.

L.H.S. = sec²A × 1/sec²A

L.H.S. = 1

and, R.H.S. = 1

.°. (1 + tan² A) (1 + sin A) (1 - sin A) = 1

Hence, L.H.S. = R.H.S.