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I need help solving both problems. Can someone please solve them? Thanks

I need help solving both problems. Can someone please solve them? Thanks

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Grade:11

1 Answers

Aditya Gupta
2081 Points
5 years ago
Let cosx=y
cos2x+cosx= 2y^2+y-1=f(y) suchthat y lies in -1 to 1.
Now find f(1), f(-1) and then differentiate f(y) and set it to zero to obtain y=-1/4. Find f(-1/4). Compare these three values and the least one of them is the minimum value.
For the first question, write sin^2x and cos^2x in terms of cos2x and sinx-cosx as sin2x/2 and then set 2x=y. Having done this, use the fact that asinx+bcosx lies in -√(a^2+b^2) to √(a^2+b^2).

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