Advertisements
Advertisements
Question
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
Advertisements
Solution
Given:
`sin ^2θ cos^2 θ(1+tan^2 θ)(1+cot ^2θ)=λ`
`⇒ sin^2θ cos^2 θ sec^2 θ cosec^2θ=λ`
⇒`(sin^2 θ cosec^2θ )xx (cos^2θ sec^2 θ)= λ`
⇒ `(sin^2θ xx 1/sin^2θ )(cos^2 θxx1/cos^2θ)=λ`
\[\Rightarrow \lambda = 1 \times 1 = 1\]
APPEARS IN
RELATED QUESTIONS
Prove that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
Prove the following trigonometric identities.
`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Write the value of cosec2 (90° − θ) − tan2 θ.
Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\]
If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =
If cos A + cos2 A = 1, then sin2 A + sin4 A =
Prove the following identity :
tanA+cotA=secAcosecA
Prove the following identity:
tan2A − sin2A = tan2A · sin2A
Prove the following identity :
`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Find x , if `cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`
If x = h + a cos θ, y = k + b sin θ.
Prove that `((x - h)/a)^2 + ((y - k)/b)^2 = 1`.
If x = a tan θ and y = b sec θ then
Prove that `cot^2 "A" [(sec "A" - 1)/(1 + sin "A")] + sec^2 "A" [(sin"A" - 1)/(1 + sec"A")]` = 0
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
If 3 sin θ = 4 cos θ, then sec θ = ?
If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`
Prove the following identity:
(sin2θ – 1)(tan2θ + 1) + 1 = 0
