Direction: Study the following questions carefully and choose the right answer:
Important for :
1
If sin A = 3/5 and A is an acute angle, then tan A + sec A is equal to
» Explain it
C
 sin A = 3 5

we know that,

cos2 A = 1 – sin2 A

∴ cos A =
 1 – 9 25
=
 16 25
=  4
5

 ∴   tan A + sec A = sin A + 1 cos A cos A

=
 sin A + 1 cos A
=
 3 + 1 5
 4 5

 = 8 × 5 = 2. 5 4

Hence, option C is correct.

2
 What is the value of tan A – sin A ? sin3 A
» Explain it
C
 sin A – sin A tan A – sin A = cos A sin3 A sin3 A

 sin A ( 1 – 1 ) = cos A sin3 A

 ( 1 – cos A ) = cos A sin2 A

 = ( 1 – cos A ) cos A.sin2 A

 = 1 – cos A cos A (1 – cos2 A)

 = 1 – cos A cos A (1 – cosA) (1 + cos A)

 = 1 . 1 = sec A cos A 1 + cos A 1 + cos A

Hence, option C is correct.

3
(1 – tan A)2 + (1 + tan A)2 + (1 – cot A)2 + (1 + cot A)2 is equal to
» Explain it
C
(1 – tan A)2 + (1 + tan A)2 + (1 – cot A)2 + (1 + cot A)2

= 1 + tan2 A – 2 tan A + 1 + tan2 A + 2 tan A + 1 + cot2 A – 2 cot A + 1 + cot2 A + 2 cot A

= 1 + tan2 A + 1 + tan2 A + 1 + cot2 A + 1 + cot2 A

= sec2 A + sec2 A + cosec2 A + cosec2 A

[     1 + tan2 A = sec2 A    and    1 + cot2 A = cosec2 A   ]

= 2 (sec2 A + cosec2 A)

 = [ 1 + 1 ] =  2 [ sin2A + cos2A ] cos2 A sin2 A sin2 A.cos2 A

 =  2 × 1 =  2 sec2 A.cosec2A sin2 A.cos2 A

Hence, option C is correct.

4
If α, β and γ are acute angles such that sin α = (3 / 2), cos β = (3 / 2) and tan γ = 1, then what is α + β + γ equal to?
» Explain it
C
sin α =
 3

2

⇒ sin α = sin 60°

⇒  α = 60°

cos β =
 3

2

⇒ cos β = cos 30°

⇒ β = 30°

and tan γ = 1   ⇒  γ = 45°

∴    α +β + γ = 60° + 30° + 45° = 135°.

Hence, option C is correct.

5
If cos A + cosA = 1, then what is the value of 2(sin2 A + sin4 A)?
» Explain it
B
cos A + cos2 A = 1

cos A = 1 – cos2 A = sin2 A         ...(i)

Now,  2(sin2 A + sin4 A) = 2(sin2 A + cos2 A)

[ from eq.(i) sin2 A = cos A, then sin4 A = cos2 A ]

= 2 × 1 = 2.

Hence, option B is correct.