Ex 3.3, 9 - Chapter 3 Class 11 Trigonometric Functions

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Ex 3.3, 9 Prove cos (3 /2+ ) cos (2 + )[cot (3 /2 ) + cot (2 + )] =1 Taking L.H.S. First we solve cos (3 /2 "+ " ) Putting = 180 = cos ((3 180 )/2 " + x" ) = cos ( 270 + x ) = cos ( 360 90 + x ) = cos (2 90 + x ) = cos (2 + (x 90 )) = cos (x 90 ) = cos ( (90 x)) = cos (90 x) = sin x Now cos (2 + x) = cos x & cot (2 + x) = cot x Now we solve cot (3 /2 " " x) Putting = 180 = cot ((3 180 )/2 " x" ) = cot ( 270 " " x ) = cot ( 360 90 " " x ) = cot (2 " " 90 " " x ) = cot (2 " " (x + 90 )) = " " cot (x + 90 ) = ( tan x) = tan x Now putting values in equation cos (3 /2+ ) cos (2 + )[cot (3 /2 ) + cot (2 + )] = (sin x) (cos x) [tan x + cot x] = (sin x cos x) [cot x + tan x] = (sin x cos x) [cos /sin " " + sin /cos ] = (sin x cos x) [( (cos ) (cos )+ (sin ) (sin ))/(sin (cos ))] = (sin x cos x) [(cos2 + sin2 )/(sin (cos ))] = cos2 + sin2 = 1 = R.H.S Hence proved