Question

(sin 22*1/2degree + cos 22*1/2 degree)raise4 =?

degree

Answer 1

im assuming the question to be, `(sin (22 1/2)^@ + cos (22 1/2)^@)^4`

`=> (color(green)((sin (45/2)^@ + cos (45/2)^@)^2))^2`

apply basic algebraic identity, `color(green)((a+b)^2 = a^2+b^2 +2ab`

`=> [color(red)(sin^2 (45/2)^@ + cos^2 (45/2)^@) + color(magenta)(2sin (45/2)^@cos (45/2)^@)]^2`

now, `color(red)(sin^2x + cos^2x = 1) and color(magenta)(sin2x = 2sinxcosx`

`=> (1 + sin (cancel2xx45/cancel2)^@)^2`

`=> (1+sin45^@)^2`

`=> color(green)((1+1/sqrt2)^2`

again, apply, `color(green)((a+b)^2 = a^2+b^2 +2ab`

`=> 1+1/2 + 2/sqrt2`

`=> 3/2 + sqrt2`