Advertisements
Advertisements
प्रश्न
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S = `square`
= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
= `1/(sintheta*costheta)` ......`[cos^2theta + sin^2theta = square]`
= `1/sintheta xx 1/square`
= `square`
= R.H.S
Advertisements
उत्तर
L.H.S = cot θ + tan θ
= `costheta/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/(sintheta*costheta)`
= `1/(sintheta*costheta)` ......[cos2θ + sin2θ = 1]
= `1/sintheta xx 1/costheta`
= cosecθ × secθ
= R.H.S.
APPEARS IN
संबंधित प्रश्न
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove the following trigonometric identities
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
`(1+ cos theta + sin theta)/( 1+ cos theta - sin theta )= (1+ sin theta )/(cos theta)`
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`
If sec θ = x + `1/(4"x"), x ≠ 0,` find (sec θ + tan θ)
Prove that sin θ sin( 90° - θ) - cos θ cos( 90° - θ) = 0
Prove that `(cot "A" + "cosec A" - 1)/(cot "A" - "cosec A" + 1) = (1 + cos "A")/sin "A"`
`5/(sin^2theta) - 5cot^2theta`, complete the activity given below.
Activity:
`5/(sin^2theta) - 5cot^2theta`
= `square (1/(sin^2theta) - cot^2theta)`
= `5(square - cot^2theta) ......[1/(sin^2theta) = square]`
= 5(1)
= `square`
If tan θ = `9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ......[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
If 2sin2β − cos2β = 2, then β is ______.
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
