Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
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 trigonometric identities.
sin2 A cos2 B − cos2 A sin2 B = sin2 A − sin2 B
If cos θ + cos2 θ = 1, prove that sin12 θ + 3 sin10 θ + 3 sin8 θ + sin6 θ + 2 sin4 θ + 2 sin2 θ − 2 = 1
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
2 (sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) is equal to
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Prove the following identity :
`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ`
Prove the following identity :
`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Prove that cosec2 (90° - θ) + cot2 (90° - θ) = 1 + 2 tan2 θ.
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
