Advertisements
Advertisements
प्रश्न
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
Prove that: tan θ + cot θ = sec θ cosec θ
Advertisements
उत्तर
L.H.S. = cot θ + tan θ
L.H.S. = `costheta/sintheta + sintheta/costheta`
L.H.S. = `(cos^2theta + sin^2theta)/(sintheta costheta)`
[cos2 θ + sin2 θ = 1]
L.H.S. = `1/(sintheta costheta)`
Use Reciprocal Identities:
The expression can be split into `(1/sin θ) xx (1/cos θ)`.
`1/sin θ` = cosec θ
`1/cos θ` = sec θ
L.H.S. = cosec θ.sec θ
L.H.S. = sec θ.cosec θ
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Express the ratios cos A, tan A and sec A in terms of sin A.
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Prove that
`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
`(1+ cos theta - sin^2 theta )/(sin theta (1+ cos theta))= cot theta`
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
Write the value of sin A cos (90° − A) + cos A sin (90° − A).
Write True' or False' and justify your answer the following:
\[ \cos \theta = \frac{a^2 + b^2}{2ab}\]where a and b are two distinct numbers such that ab > 0.
Prove that:
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Prove the following identity :
`(1 + sinA)/(1 - sinA) = (cosecA + 1)/(cosecA - 1)`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
Prove that `(sin^2θ)/(cos θ) + cos θ = sec θ`.
Prove that `(cosθ)/(1 + sinθ) = (1 - sinθ)/(cosθ)`.
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
