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प्रश्न
If tan θ = `x/y`, then cos θ is equal to ______.
विकल्प
`x/sqrt(x^2 + y^2)`
`y/sqrt(x^2 + y^2)`
`x/sqrt(x^2 - y^2)`
`y/sqrt(x^2 - y^2)`
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उत्तर
If tan θ = `x/y`, then cos θ is equal to `underlinebb(y/sqrt(x^2 + y^2))`.
Explanation:
Given, tan θ = `x/y` ...(i)
We know that
tan θ = `"Perpendicular (P)"/"Base (B)"` ...(ii)
By comparing equations (i) and (ii), we get
P = x, B = y
H2 = P2 + B2 ...(Pythagoras theorem)
H2 = x2 + y2
H = `sqrt(x^2 + y^2)`
Then cos θ = `B/H`
= `y/sqrt(x^2 + y^2)`
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संबंधित प्रश्न
Prove the following trigonometric identities.
`((1 + sin theta - cos theta)/(1 + sin theta + cos theta))^2 = (1 - cos theta)/(1 + cos theta)`
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos ^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle.
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.
