Question

40 = 90^2/16 sinx cosx find x

Answer 1

x = 4.545

Explanation:

Given the expression

`40=(90^2)/(16) sinxcosx\\\\Cross\ multiplying;\\\\16*40 = 90^2 sinxcosx\\\\640 = 90^2 sinxcosx\\\\(640)/(8100) = sinxcosx\\ from\ trig\ identity, sin2x = 2sinxcosx\\sinxcosx = sin2x/2\\`

`Hence, \ (640)/(8100) = (sin2x)/(2) \\\\(2*640)/(8100) = sin2x\\ \\(1280)/(8100)=sin2x\\ \\0.158 = sin2x\\\\2x = sin^(-1) 0.158\\\\2x = 9.09\\x = 9.09/2\\x =4.545`