Direction: Study the following questions carefully and choose the right answer:
Important for :
1
If tan Θ = 3 and 0 < Θ < 2π(pi), find the values of Θ.
» Explain it
C
 tan Θ = √3 = tan π ⇒ Θ = π . 3 3

But, tan Θ = tan (π + Θ).

 So, tan π = tan ( π + π ) 3 3

 = tan 4π 3

Hence, the required values of Θ =

 π and 4π . 3 3

Hence, option C is correct.

2
What is the value of sin2 60° + cos230°+ cot2 45° + sec2 60° – cosec2 30° + cos2 0°.
» Explain it
C
Hence, option C is correct.
3
If tan 62° = p/q find the value of tan 28° .
» Explain it
B
tan 28° = (tan 90° - 62°) =

 cot 62° = q p

Hence, option B is correct.

4
If x2 + y2 + z2 = r2 and x = r cos A sin B, y = r sin A sin B, find the value of z.
» Explain it
B
x2 + y2

= r2 cos2 A sin2 B + r2 sin2 A sin2 B

=  r2 sin2 B (cos2 A + sin2 A)

= r2 sin2 B.

Now

x2 + y2 + z2  =  r2

⇒  z2 = r2 – (x2 + y2)

∴ z2 = r2 – rsin2 B

= r2 (1 – sin2 B)

= r2 cos2 B Hence, z = r cos B.

Hence, option B is correct.

5
If 8 tan x = 15, the value of (sin x - cos x) is:
» Explain it
C
 tan x = 15 8

∴  sec x = 1 + tan2 x

 1 + 225 64
=
 289 64
=  17
8

∴ cosec x = 1 + cot2 x

=
 1 + 64 225
=
 289 225
=  17
15

 ∴ cos x = 8 and sin x = 15 17 17

 So, (sin x - cos x) = ( 15 _ 8 ) 17 17

 = 7 17

Hence, option C is correct.