Question

prove that cos10.cos50.cos70=√3/8​

Answer 1

Answer:

Step-by-step explanation

= (cos 10 cos 50) cos70

=1/2(2cos10cos50)cos70

=1/2{(cos(50+10) +cos(50-10)} cos70

=1/2(cos60+ cos40) cos70. we know cos 60 value is 1/2. so this value will put in the next step

=1/2(1/2+cos40)cos70

=1/2(cos70/2 +cos70cos40)

=1/2(cos70 +cos70 cos40/2) take LCM

=1/4(cos70+ 2 cos70cos40)

=1/4(cos70+ cos110+ cos30)

=1/4(cos70+cos(180-70)+ cos30)

=1/4(cos70-cos70 +cos30) { -cos 70 is in 2nd quadrant.}

=1/4×√3/2

=√3/8

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