Advertisements
Advertisements
Question
Prove the following trigonometric identities.
`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta)/cos theta`
Advertisements
Solution
We have to prove the following identity
`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta)/cos theta`
Consider the LHS = `(1 + cos theta + sin theta)/(1 + cos theta - sin theta)`
`= ((1 + cos theta + sin theta)/(1 + cos theta - sin theta))((1 + cos theta + sin theta)/(1 + cos theta + sin theta))`
`= (1 + cos theta + sin theta)^2/((1 + cos theta)^2 sin^2 theta)`
`= (2 + 2(cos theta + sin theta + sin theta cos theta))/(2 cos^2 theta + 2 cos theta)`
`= (2(1 + cos theta)(1 + sin theta))/(2 cos theta (1 + cos theta))`
`= (1 + sin theta)/cos theta`
= RHS
Hence proved
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
` tan^2 theta - 1/( cos^2 theta )=-1`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
Find the value of `(cos 38° cosec 52°)/(tan 18° tan 35° tan 60° tan 72° tan 55°)`
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.
sin2θ + sin2(90 – θ) = ?
Show that tan4θ + tan2θ = sec4θ – sec2θ.
