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`        Proof that Cos2x+asin2x=cosx-sinx and find the value of a `
one year ago

Varun
28 Points
```							Explanation:cosx+sinx=cos2x+sin2x . ∴cosx−cos2x=sin2x−sinx . ∴−2sin(x+2x2)sin(x−2x2)=2cos(2x+x2)sin(2x−x2). ∴+sin(32x)sin(+12x)=cos(32x)sin(12x). ∴sin(32x)sin(12x)−cos(32x)sin(12x)=0. ∴sin(12x)[sin(32x)−cos(32x)]=0 . ∴sin(12x)=0,or,sin(32x)=cos(32x). Case 1 :  sin(12x)=0 . sin(12x)=0⇒12x=kπ⇒x=2kπ,k∈Z. Case 2 :  sin(32x)=cos(32x) . Note that  cos(32x) can not be 0,  because, in that case, by the virtue of the eqn.,  sin(32x) will also be 0, contradicting, sin2(32x)+cos2(32x)=1 . So, dividing by  cos(32x)≠0 , we get, tan(32x)=1=tan(π4), giving,   32x=kπ+π4⇒x=23kπ+π6=(4k+1)π6,k∈Z. Altogether, The Soln. Set = {2kπ}∪{(4k+1)π6},k∈Z .
```
one year ago
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### Course Features

• 31 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions