CBSE Class 10 Answered
a cos theta + b sin theta = 5 find value of b cos theta - a sin theta?
Asked by Soma | 28 Feb, 2019, 15:45: PM
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 = x2 ... (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](https://images.topperlearning.com/topper/tinymce/cache/3bad0184028762f21c0ada584d11fed9.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/3bad0184028762f21c0ada584d11fed9.png)
Answered by Yasmeen Khan | 28 Feb, 2019, 16:50: PM
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