Question

Root3 sinx - cosx =2

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

√cosx=2−sinx  

3cos2x=4−sin2x−4sinx

4sinx=4−sin2x−3cos2x=4+sin2x−3(1−sin2x)=1+4sin2x

0=4sin2x−4sinx+1

That’s a quadratic in sinx. It factors; it’s actually a perfect square.

(2sinx−1)2=0

sinx=12

x=π/6+2πk or x=5π/6+2πk, both for integer k

We have to check both, and cos5π/6=−3–√/2 gives a left hand side of −1 in the original question, which doesn’t check. So we’re left with

x=π/6+2πk

Check:

cosx=3–√/2  

sinx=1/2  

3–√cosx+sinx=3–√⋅3–√/2+1/2=2