Advertisements
Advertisements
प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
उत्तर
L.H.S
= `sqrt((1+sinA)/(1-sinA))`
= `sqrt(((1+sinA)(1+sinA))/((1-sinA)(1+sinA))`
= `(1+sinA)/(sqrt(1-sin^2A))`
= `(1+sinA)/sqrt(cos^2A)`
= `(1+sinA)/cosA`
= secA + tan A
= `1/cos A + sin A/cos A`
= R.H.S
APPEARS IN
संबंधित प्रश्न
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
`(sintheta - 2sin^3theta)/(2costheta - costheta) =tan theta`
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
Prove that:
`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
`1/((1+ sintheta ))+1/((1- sin theta ))= 2 sec^2 theta`
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
If `sec theta = x ,"write the value of tan" theta`.
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
Write True' or False' and justify your answer the following :
The value of \[\sin \theta\] is \[x + \frac{1}{x}\] where 'x' is a positive real number .
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Prove the following identity :
`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
Find A if tan 2A = cot (A-24°).
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove that cos θ sin (90° - θ) + sin θ cos (90° - θ) = 1.
Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
Prove that : `tan"A"/(1 - cot"A") + cot"A"/(1 - tan"A") = sec"A".cosec"A" + 1`.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?
Prove that `(1 + sec "A")/"sec A" = (sin^2"A")/(1 - cos"A")`
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
