Simplify. $cos(36° − A) cos(3

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

Simplify.

$cos(36° − A) cos(36° + A) + cos(54° − A) cos(54° + A)$

Options:

cos A

sin 2A

cos 2A

sin A

Correct Answer:

cos 2A

Explanation:

cos (36° - A ) . cos ( 36° + A ) + cos (54° - A ). cos (54° + A )

{ using concept , sinA = cos ( 90° - A ) }

= cos (90° - ( 36° - A ) ) . cos ( 90° - ( 36°+ A ) ) + cos (90° (54° - A ) ). cos (54° + A )

= sin ( 54°+A ) . sin ( 54° - A ) + cos (54° - A ). cos (54° + A )

{ using concept , cos (A - B) = sinA.sinB + cosA.cosB }

= cos ( 54° + A - 54° + A )

= cos (2A)