EXERCISE 8.4
Q.4) Choose the correct option. Justify your choice.
(i) 9 sec2 A – 9 tan2 A =
Justification:
9 sec2A – 9 tan2A
=
9
(sec2A
–
tan2A)
=
9
(1)
=
9
sec2θ – tan2θ = 1
9 sec2A – 9 tan2A
∴
Hence, option (B) is correct.
[Q sec2θ – tan2θ = 1]
(A) 1 (B) 9 (C) 8 (D) 0
EXERCISE 8.4
Q.4) Choose the correct option. Justify your choice.
=
1 + tan2 A
1 + cot2 A
(iv)
Justification:
1 + tan2A
1 + cot2A
=
sec2A
cosec2A
=
1
cos2A
÷
1
sin2A
=
1
cos2A
1
sin2A
×
=
sin2 A
cos2A
tan2 A
=
1 + tan2θ = sec2θ
1 + cot2θ = cosec2θ
∴
1 + tan2 A
1 + cot2 A
Hence, option (D) is correct.
(A) sec2 A (B) – 1 (C) cot2A (D) tan2A
EXERCISE 8.4
Q.4) Choose the correct option. Justify your choice.
(iii) (sec A + tan A) (1 – sin A) =
Justification:
(sec A + tan A)
(1 – sin A)
=
1
cos A
+
cos A
sin A
(1 – sin A)
=
(1
+
sin A)
cos A
(1 – sin A)
=
–
sin2 A
cos A
=
cos A
=
cos A
=
cos A
1
cos2A
1 – sin2θ = cos2θ
∴
(sec A + tan A) (1 – sin A)
Hence, option (D) is correct.
[Q cos2θ = 1 – sin2θ]
(A) sec A (B) sin A (C) cosec A (D) cos A