QJEEM19Mae416: JEE Main 2019 Mathematics - Class 11 JEEM19Mae416 Solution: The value of cos 2 10° – cos10°cos50° + cos 2 50° is

Question

Verified Solution • 2025–26 Session moderate

The value of cos²10° – cos10°cos50° + cos²50° is

Accepted Answer

cos²10° – cos10°cos50° + cos²50°

=

\frac{1}{2}

[ 2cos²10° – 2cos10°cos50° + 2cos²50°]

=

\frac{1}{2}

[ 1 + cos20° - cos60° - cos40° + 1 + cos100°]

=

\frac{1}{2}

[ 2 -

\frac{1}{2}

+ cos20° + cos100° - cos40°]

=

\frac{1}{2}

[

\frac{3}{2}

+ 2cos60°cos40° - cos40°]

=

\frac{1}{2}

[

\frac{3}{2}

+ cos40° - cos40°]

=

\frac{3}{4}

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