Math, asked by yeshaaco25, 2 months ago

$\sin(\pi \div6 \times a) \times \sin(\pi \div 3 \times b) - \cos(\pi \div 6 \times a) \times \sin(\pi \div 3 \times b)$

Answers

Answered by nancy359

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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

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