Question

If 2 sin (3x – 15)° = root3, find the value of
sin^2 (2x + 10)° + tan^2 (x + 5)º​

Answer 1

Answer:

2sin(3x-15)° =√3

2sin(3x-15)° =2*√3/2

2sin(3x-15)° =2sin60°

on comparing

3x-15 = 60

3x = 60+15

3x = 75

x = 75/3

(x = 25)

sin^2(2x+10) + tan^2(x+5)

put the value of x

sin^2 (60) + tan^2 (30)

(√3/2)^2 +(1/√3)^2

3/4 +1/3

take LCM

9+4/12=13/12

Answer 2

Answer:

2sin(3x-15)°=√3

=> sin(3x-15)°=√3/2

But,

sin 60°=√3/2

.

. . Sin60°=sin(3x-15)°

=> 60°=(3x-15)°

=>3x=60°+15°

=>3x=75°

=> x=25°

* Sin^2(2x+10)° + tan^2(x+5)°

=>Sin^2(50+10)° + tan^2(25+5)°

=>Sin^2(60)° + tan^2(30)°

=>(√3/2)^2 + (1/√3)^2

=>3/4 + 1/3

=>(9+4)/12

=>13/12