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  • The value of <img alt="cos^{2}10^{\circ}-cos10^{\circ}cos50^{\circ}+cos^{2}50^{\circ}" src="http://entrancecorner.oncodecogs.com/gif.latex?cos%5E%7B2%7D10%5E%7B%5Ccirc%7D-cos10%5E%7B%5Ccirc%7Dcos50

The value of cos^{2}10^{\circ}-cos10^{\circ}cos50^{\circ}+cos^{2}50^{\circ} is equal to (up to 2 decimal)

Option: 1

1.34


Option: 2

0.34


Option: 3

0.75


Option: 4

3


Answers (1)

best_answer

As we have learnt in

 

Transformation Formulae -

- wherein

These formula are also called A-B formulae.

 

 

Double Angle Formula -

Double angle formula

- wherein

These are formulae for double angles.

 

 

cos^{2}10^{\circ}-cos10^{\circ}cos50^{\circ}+cos^{2}50^{\circ}

=\frac{1}{2} \left [ 1+cos 20^{\circ}-\left ( cos60^{\circ} +cos40^{\circ}\right )+\left ( 1+ cos100^{\circ} \right )\right ]

=\frac{1}{2} \left [ 1+cos 20^{\circ}-\frac{1}{2}- cos40^{\circ} + 1- cos80^{\circ} \right ]

=\frac{1}{2} \left [ \frac{3}{2}+cos 20^{\circ}-(2cos60^{\circ} cos20^{\circ}) \right ]=\frac{3}{4}

Posted by

Shailly goel

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