Advertisements
Advertisements
प्रश्न
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
Advertisements
उत्तर
secθ + tanθ = `1/cosθ + sintheta/cosθ`
`=(1+sintheta)/costheta`
`=((1+sintheta)(1-sintheta))/(costheta (1-sintheta))`
`=(1^2 - sin^2theta)/(costheta(1-sintheta))`
`=cos^2theta/(costheta(1-sintheta))`
`therefore sectheta +tantheta =costheta/(1-sintheta)`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2 = 2`
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`
Write the value of cosec2 (90° − θ) − tan2 θ.
Write the value of sin A cos (90° − A) + cos A sin (90° − A).
The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Prove the following identity :
`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`
Without using trigonometric identity , show that :
`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`
Without using trigonometric identity , show that :
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
If x = a tan θ and y = b sec θ then
If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ, then prove that x2 + y2 = 1
If 2 cos θ + sin θ = `1(θ ≠ π/2)`, then 7 cos θ + 6 sin θ is equal to ______.
