Advertisements
Advertisements
प्रश्न
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
Advertisements
उत्तर
secθ + tanθ = `1/cosθ + sintheta/cosθ`
`=(1+sintheta)/costheta`
`=((1+sintheta)(1-sintheta))/(costheta (1-sintheta))`
`=(1^2 - sin^2theta)/(costheta(1-sintheta))`
`=cos^2theta/(costheta(1-sintheta))`
`therefore sectheta +tantheta =costheta/(1-sintheta)`
APPEARS IN
संबंधित प्रश्न
If tanθ + sinθ = m and tanθ – sinθ = n, show that `m^2 – n^2 = 4\sqrt{mn}.`
Without using trigonometric tables evaluate
`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80^@)`
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Prove the following identities:
`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`
If `(cosec theta - sin theta )= a^3 and (sec theta - cos theta ) = b^3 , " prove that " a^2 b^2 ( a^2+ b^2 ) =1`
If ` cot A= 4/3 and (A+ B) = 90° ` ,what is the value of tan B?
Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`
Write the value of cosec2 (90° − θ) − tan2 θ.
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 :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
Prove the following identity :
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Without using the trigonometric table, prove that
tan 10° tan 15° tan 75° tan 80° = 1
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.
If tan θ = `7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ......[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
cos θ = `square` .......`[cos theta = 1/sectheta]`
Prove that
sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A
Prove the following that:
`tan^3θ/(1 + tan^2θ) + cot^3θ/(1 + cot^2θ)` = secθ cosecθ – 2 sinθ cosθ
