Question

please explain
$a + b + c = 3\pi \div 2 then cos2 a + cos2b + cos2c is equal to$

Answer 1

Hey !!!

a + b + c = 3π/2 = 270°

a + b = 270° - c _______1)

From given :

=> cos2a + cos2b+ cos2c

=> we know a formula

cosc + cosd = 2cos(c + d)/2 × cos ( c -d)/2

using this formula

2cos ( 2a + 2b)/2 ×cos ( 2c + 2d)/2 + cos2c

↘we know cos2C = 1 - 2sin²C

or, 2cos (a + b) cos (a - b) + 1 - 2sin²c

or, 2cos (270° - c) cos ( a - b) + 1 - 2sin²c

[cos ( 270 - c ) = sinc ] from 1st

or, -2sinc cos ( a - b)+ 1 - 2sin²c

or, - 2sinc cos ( a - b) - 2sin²c + 1

or, - 2sinc { cos (a - b) + sinc} + 1

from 1st sinc = -cos ( a + b)

or, - 2sinc { cos ( a + b) - cos ( a - b) } + 1

now ,
we know that , .
cosc - cosd = 2sin(c+d)/2*sin(c-d) using here

or, -2sinc { 2sin (a + b + a - b)/2 ) ×sin(a + b - a + b)/2 + 1

or, 1 - 2sinc ( 2sina sinb)

or, 1 - 4sinc sina sinb

or, 1 - 4sina sinb sinc Answer ✔prooved ♻
______________________

Hope it helps you !!!

@Rajukumar111

Answer 2

Answer:

hope u got the answer with proper solution