Advertisements
Advertisements
प्रश्न
Prove the following identities:
`(sin theta + 1 - cos theta)/(cos theta - 1 + sin theta) = (1 + sin theta)/(cos theta)`
Advertisements
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
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec2 A = 1 cot2 A.
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following identities:
(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
If `sin theta = x , " write the value of cot "theta .`
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
Write 'True' or 'False' and justify your answer in the following:
\[\cos \theta = \frac{a^2 + b^2}{2ab}\], where a and b are two distinct numbers such that ab > 0.
If \[sec\theta + tan\theta = x\] then \[tan\theta =\]
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
If x = acosθ , y = bcotθ , prove that `a^2/x^2 - b^2/y^2 = 1.`
Prove that:
tan (55° + x) = cot (35° – x)
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ.
Prove that `(cot A)/(1 - cot A) + (tan A)/(1 - tan A) = -1`.
sec θ when expressed in term of cot θ, is equal to ______.
