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Answer» The answer is GIVEN below :
Trigonometry is the study of angles and its ratios. This study prescribes the RELATION amongst the sides of a triangle and angles of the triangle.
There are sine, cosine, tangent, cot, sectant and cosec ratios to an angle of a triangle.
Let me tell you an interesting fact about Trigonometry.
"Triangle" > "Trigonometry"
Remember some formulae now :
sin²θ + cos²θ = 1
sec²θ - tan²θ = 1
cosec²θ - cot²θ = 1
Want to learn more!
Here it is :
sin(A + B) = sinA cosB + cosA sinB
sin(A - B) = sinA cosB - cosA sinB
COS(A + B) = cosA cosB - sinA sinB
cos(A - B) = cosA cosB + sinA sinB
SOLUTION :
Now, cos(5π/3) × cos(37π/6)
= cos[(5 × 180)/3]° × cos[(37 × 180)/3]°
= cos300° × cos2220°
= cos(360° - 60°) × cos{(360° × 6) + 60°}
= cos60° × cos60°,
since cos(2nπ ± θ) = cosθ, where n = 1, 2, 3, ...
= ½ × ½, since cos60° = ½
= ¼
Thank you for your QUESTION.
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