Advertisements
Advertisements
प्रश्न
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
उत्तर
LHS= `(sin theta+1cos theta)/(cos theta-1+sin theta) `
=`((sin theta+1-cos theta)(sin theta+cos theta+1))/((cos theta -1 + sin theta)(sin theta + cos theta +1))`
=`((sin theta + 1 )^2 - cos^2 theta)/((sin theta + cos theta )^2 -1^2)`
=`(sin^2 theta +1+2 sin theta - cos^2 theta)/(sin^2 + cos^2 theta+2 sin theta cos theta -1)`
=`(sin^2 theta + sin^2 theta + cos^2 theta +2sin theta - cos^2 theta)/(2 sin theta cos theta)`
=`(2 sin ^2 theta + 2 sin theta)/(2 sin theta cos theta)`
=`(2 sin theta (1+ sin theta))/(2 sin theta cos theta)`
=`(1+sin theta)/cos theta`
= RHS
APPEARS IN
संबंधित प्रश्न
If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
`"If "\frac{\cos \alpha }{\cos \beta }=m\text{ and }\frac{\cos \alpha }{\sin \beta }=n " show that " (m^2 + n^2 ) cos^2 β = n^2`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
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.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA cosecA + 1`
`cot^2 theta - 1/(sin^2 theta ) = -1`a
If `sec theta = x ,"write the value of tan" theta`.
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
Prove the following identity :
`cosA/(1 + sinA) = secA - tanA`
Find the value of ( sin2 33° + sin2 57°).
Prove that `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2 = sin A.cos A`
If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1
The value of sin2θ + `1/(1 + tan^2 theta)` is equal to
If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
Prove that `(tan(90 - theta) + cot(90 - theta))/("cosec" theta)` = sec θ
Prove that `(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
If sin A = `1/2`, then the value of sec A is ______.
