Advertisements
Advertisements
प्रश्न
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S = `square`
= `cos^2theta xx square .....[1 + tan^2theta = square]`
= `(cos theta xx square)^2`
= 12
= 1
= R.H.S
Advertisements
उत्तर
L.H.S. = `cos^2theta*(1 + tan^2theta)`
= `cos^2theta xx sec^2theta` .....`[1 + tan^2theta = sec^2theta]`
= `(cos theta xx sectheta)^2`
= 12
= 1
= R.H.S
APPEARS IN
संबंधित प्रश्न
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
Prove the following trigonometric identities.
`[tan θ + 1/cos θ]^2 + [tan θ - 1/cos θ]^2 = 2((1 + sin^2 θ)/(1 - sin^2 θ))`
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Prove the following identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
What is the value of (1 + cot2 θ) sin2 θ?
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Prove the following identity :
`(cos^3θ + sin^3θ)/(cosθ + sinθ) + (cos^3θ - sin^3θ)/(cosθ - sinθ) = 2`
If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn
If tan θ = 2, where θ is an acute angle, find the value of cos θ.
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
If tan θ = `13/12`, then cot θ = ?
Prove that `sec"A"/(tan "A" + cot "A")` = sin A
Prove that
sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A
