Question

How is (1-sinx)(-7sinx)-(7cosx)(-cosx) equal to 7(1-sinx)?
PLEASE HELP

Answer 1

[1 - sin(x)][-7sin(x)] - [7cos(x)][-cos(x)] = 7[1 - sin(x)]
-7sin(x)[1] + 7sin(x)[sin(x)] + 7cos²(x) = 7[1] - 7[sin(x)]
-7sin(x) + 7sin²(x) + 7cos²(x) = 7 - 7sin(x)
-7sin(x) + 7 = 7 - 7sin(x)

It is equal by knowing that it has the same number and trigonometric function 1 - sin(x) in order to help us solve the answer to this equation.

Answer 2

so to write it out using order of operations it would be -7sinx+7sin^2x-(-7cos^2x). This would then equal 7-7sinx which can be simplified to 7(1-sinx). the way you were able to get rid of the cos^2x and the sin^2x is because cos^2x+sin^2x=1.