मराठी
महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

(sec θ + tan θ) . (sec θ – tan θ) = ?

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प्रश्न

(sec θ + tan θ) . (sec θ – tan θ) = ?

बेरीज
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उत्तर

(sec θ + tan θ)(sec θ – tan θ)

= sec2θ – tan2θ   ...[∵ (a + b)(a – b) = a2 – b2]

= 1   ...`[(∵ 1 + tan^2θ = sec^2θ),(∴ sec^2θ - tan^2θ = 1)]`

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पाठ 6: Trigonometry - Exercise

संबंधित प्रश्‍न

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.

`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`


Prove the following trigonometric identities.

(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A


(i)` (1-cos^2 theta )cosec^2theta = 1`


`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec  theta)`


` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`


Find the value of sin ` 48° sec 42° + cos 48°  cosec 42°`

 


Prove the following identity :

`(1 - sin^2θ)sec^2θ = 1`


Prove the following identity : 

`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`


Prove the following identity : 

`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq


Prove the following identity :

`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`


Prove the following identity : 

`(1 + cotA + tanA)(sinA - cosA) = secA/(cosec^2A) - (cosecA)/sec^2A`


Find the value of `θ(0^circ < θ < 90^circ)` if : 

`cos 63^circ sec(90^circ - θ) = 1`


Without using trigonometric identity , show that :

`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`


If cosθ = `5/13`, then find sinθ. 


Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.


Prove that `sin A/(sec A + tan A - 1) + cos A/("cosec"  A + cot A - 1) = 1`.


Prove that `(sin θ + "cosec"  θ)/(sin θ) = 2 + cot^2θ`.


Prove the following:

`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ


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