Subject
Quantitative Aptitude
Topic
Miscellaneous
If cos A + sin A = 2 cos A ,then cos A – sin A = ?
If cos A + sin A = 2 cos A ,then cos A – sin A = ?
ক)
√2sinAখ)
√2cosAগ)
0ঘ)
1Explanation
দেওয়া আছে, cos A + sin A = 2 cos A বা, (cos A + sin A) 2 = ( 2 cos A) 2 বা, cos 2 A + 2 sin A cos A + sin 2 A = 2 cos 2 A বা, (sin 2 A + cos 2 A) + 2 sin A cos A = 2 cos 2 A বা, 1 + 2 sin A cos A = 2 cos 2 A বা, 2 sin A cos A = 2 cos 2 A – 1 বা, 2 sin A cos A = 2 cos 2 A – 1 এখন, cos A – sin A = √(cos A – sin A) 2 = √(cos 2 A – 2 cos A . sin A + sin 2 A) = √{sin 2 A + cos 2 A – (2 cos 2 A – 1)} = √(sin 2 A + cos 2 A – 2 cos 2 A + 1) = √(sin 2 A – cos 2 A + 1) = √{(1 – cos 2 A) + sin 2 A} = √(sin 2 A + sin 2 A) [ sin 2 A + cos 2 A = 1 ;sin 2 A = 1 – cos 2 A ] = √(2 sin 2 A) = √2 sin ARelated questions
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