Q. 243.9( 9 Votes )

If lies in the first quadrant And cos x = 8/17, then prove that


Answer :

Given x lies in the first quadrant i.e. 0 < x < π/2 And cos x = 8/17


We know that



LHS


= cos(30 + x) + cos(45 – x) + cos(120 – x)


We know that cos(A ±B) = cosA cosB sinA sinB


= cos 30° cos x – sin 30° sin x + cos 45° cos x + sin 45° sin x + cos 120° cos x + sin 120° sin x


= cos x(cos 30° + cos 45° + cos 120°) + sin x(-sin 30° + sin 45° + sin 120°)





= RHS


Hence, proved.


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