Find x

Level pending

If $\cos^{2}{10^\circ}+\cos^{2}{50^\circ}-\sin{40^\circ}\sin{80^\circ} = x$ , what is $x$ ?

1 solution

Sanjeev Prasad
Feb 28, 2014

cos^2(10) +cos^2(50) -sin(40)sin(80) = x

L.H.S

=1/2 +cos(20) /2 +1/2 +cos(100) /2 + 1/2 ( -2 sin(40)sin(80))

=(1+ cos(20) + 1 + cos(100) + cos(120) - cos(40))/2

=(2+ (cos(20) +cos(100)) +1/2 - cos(40))/2

=( 3/2 +2 cos(60) cos(40) - cos(40))/2

=(3/2 +cos(40) - cos(40) ) /2

=3/4

=0.75

i thought that it would be convert into integer instead of 0.75/decimal

dont need scratch calculator can handle it..

Red Angel - 7 years, 2 months ago

but the answer was supposed to be submitted in decimal form. That's why i did so. Have a look on the question, above.

Sanjeev Prasad - 7 years, 2 months ago

Nice solution. Congrats.

Niranjan Khanderia - 7 years ago