a cos theta + b sin theta = 5 find value of b cos theta - a sin theta​

Asked by Soma | 28th Feb, 2019, 03:45: PM

Expert Answer:

a cos theta + b sin theta = 5 find value of b cos theta - a sin theta​
 
acosθ + bsinθ = 5   

Squaring the equation on both the sides, we get
 
a2cos2θ + b2sin2θ + 2absinθcosθ = 25   ... (i)
 
Let acosθ + bsinθ = x

Squaring the equation on both the sides, we get

a2cos2θ + b2sin2θ - 2absinθcosθ = x  ... (ii)
 
Adding (i) and (ii), we get
 

a2cos2θ + b2sin2θ + 2absinθcosθ + a2cos2θ + b2sin2θ - 2absinθcosθ  = 25 + x2

→(a2+ b2)cos2θ + (a2+ b2)sin2θ = 25 + x2
a2+ b2 = 25 + x2
→ x = begin mathsize 16px style square root of straight a squared space space plus space space straight b squared space minus space 25 space end root end style

Answered by Yasmeen Khan | 28th Feb, 2019, 04:50: PM

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