1. If tan(p+q) tan(p-q) = 1, then the value of tan p is :

(1)

(2) 1

(3)

(4)

2.  
3. Ans: (2)    tan(p+q) tan(p-q) = 1

• tan (p+q) = cot (p+q) = tan (90⁰ – (p-q))
• p+q = 90⁰ - (p-q)
• 2p = 90⁰   
• p = 45⁰ = 1

 

4. The maximum value of 24 sin + 7 cos is

(1) 7

(2) 17

(3) 24

(4) 25

5.  
6. Ans: (4) Maximum value of a sin + b cos is
7.          Required maximum value is = 25 = = 25
8.  
9. If a, b are positive acute angles, a+b 90⁰ and sin (2a - 20⁰), then the value of sec (a+b) is

(1)

(2)

(3) 1

(4) 0

 

Ans: (1)    sin (2a - 20⁰) = cos (2a - 20⁰)

• sin (2a - 20⁰) = sin (90⁰-(2b - 20⁰)) = sin (70⁰ - 2b)
• 2a-20⁰ = 70⁰-2b
• 2(a+b) = 90⁰
• a+b = 45⁰

   sec (a+b) = sec 45⁰ =

 

10. If 5 tan = 4, then the value of () is

(1)

(2)

(3)

(4)

 

Ans: (1)    5 tan = 4

• tan =

By Dividing N^r & D^r by,

= = = = =