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प्रश्न
If 4 cos2 x = 3 and x is an acute angle;
find the value of :
(i) x
(ii) cos2 x + cot2 x
(iii) cos 3x (iv) sin 2x
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उत्तर
(i) 4 cos2x = 3
cos2x = `(3)/(4)`
cos x = `(sqrt3)/(2)`
x = 30°
(ii) cos2x + cot2x = cos230° + cot230°
= `(3)/(4) + 3`
= `(15)/(4)`
= 3`(3)/(4)`
(iii) cos 3x = cos3(30°) = cos 90° = 0
(iv) sin 2x = sin 2(30°) = sin60° = `(sqrt3)/(2)`
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