Direction: Study the following questions carefully and choose the right answer:
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.