sin teta + 2cos teta =1 prove that 2sin teta - cos teta =2

Asked by manish.mayuka | 2nd May, 2021, 02:02: PM

Expert Answer:

Given:
sin theta + 2 cos theta = 1
Squaring both the sides, we get
open parentheses sinθ space plus space 2 cosθ close parentheses squared equals 1
rightwards double arrow sin squared straight theta plus 4 cos squared straight theta plus 4 sinθcosθ equals 1
rightwards double arrow 1 minus cos squared straight theta plus 4 open parentheses 1 minus sin squared straight theta close parentheses plus 4 sinθcosθ equals 1
rightwards double arrow negative cos squared straight theta plus 4 minus 4 sin squared straight theta plus 4 sinθcosθ equals 0
rightwards double arrow cos squared straight theta plus 4 sin squared straight theta minus 4 sinθcosθ equals 4
rightwards double arrow open parentheses 2 sinθ minus cosθ close parentheses squared equals 2 squared
rightwards double arrow 2 sinθ minus cosθ equals 2

Answered by Renu Varma | 5th May, 2021, 10:56: AM