Advertisements
Advertisements
प्रश्न
If tan θ = `x/y`, then cos θ is equal to ______.
पर्याय
`x/sqrt(x^2 + y^2)`
`y/sqrt(x^2 + y^2)`
`x/sqrt(x^2 - y^2)`
`y/sqrt(x^2 - y^2)`
Advertisements
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)`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities.
`((1 + sin theta - cos theta)/(1 + sin theta + cos theta))^2 = (1 - cos theta)/(1 + cos theta)`
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
Prove that cosec2 (90° - θ) + cot2 (90° - θ) = 1 + 2 tan2 θ.
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
Prove that cosec θ – cot θ = `sin theta/(1 + cos theta)`
