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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.
tan2θ cos2θ = 1 − cos2θ
Prove the following trigonometric identities
cosec6θ = cot6θ + 3 cot2θ cosec2θ + 1
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
Prove the following identities.
`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ
