The value of cos^{2}10^{\circ}-cos10^{\circ}\; cos50^{\circ}+cos^{2}50^{\circ} is:

  • Option 1)

       \frac{3}{4}+cos20^{\circ}

  • Option 2)

    3/4

  • Option 3)

    \frac{3}{2}\left ( 1+cos\; 20^{\circ} \right )

  • Option 4)

    3/2

Answers (1)

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

\Rightarrow \frac{1+cos\; 20^{\circ}}{2}+\frac{1+cos\; 100^{\circ}}{2}-cos\; 10^{\circ}\; cos\; 50^{\circ}

\Rightarrow \frac{1}{2}\left [ 2+cos\; 20\; ^{\circ} +cos\; 100^{\circ}-2cos\; 10^{\circ}\; cos\; 50^{\circ}\right ]

\Rightarrow \frac{1}{2}\left [ 2+cos\; 100^{\circ}+cos\; 20^{\circ} -cos\; 60^{\circ}-cos\; 40^{\circ}\right ]

\Rightarrow \frac{1}{2}\left [ \frac{3}{2}+2\; cos\; 60^{\circ}.cos\; 40^{\circ} -cos\; 40^{\circ}\right ]

\Rightarrow \frac{1}{2}\left [ \frac{3}{2}+2\times \frac{1}{2}\; cos\; 40^{\circ}-\;cos\; 40^{\circ} \right ]=\frac{3}{4}


Option 1)

   \frac{3}{4}+cos20^{\circ}

Option 2)

3/4

Option 3)

\frac{3}{2}\left ( 1+cos\; 20^{\circ} \right )

Option 4)

3/2

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