The general solution of $$sin10x+cos10x=2916cos42x$$ is

Correct option is 1nπ4+π8,n∈I

Questions

$The general solution of \sin^{10} x + \cos^{10} x = \frac{29}{16} \cos^{4} 2 x is$

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nπ4+π8,n∈I

nπ+π8,n∈I

nπ8+π4,n∈I

nπ+π4,n∈I

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detailed solution

Correct option is A

Sin2x5+cos2x5=2916cos42x1−cos2x25+1+cos2x25=2916cos42xput cos2x=t1−t25+1+t25=29t416⇒24t4−10t2−1=0 By inspection, t2=12cos22x=121+cos4x2=12cos4x=04x=2n+1π2x=2n+1π8,n∈Z

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The general solution of sin10x+cos10x=2916cos42x is

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$The general solution of \sin^{10} x + \cos^{10} x = \frac{29}{16} \cos^{4} 2 x is$