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CBSE Class 10 Answered

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

Asked by manish.mayuka | 02 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
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