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

(sec θ + tan θ) . (sec θ – tan θ) = ? - Geometry Mathematics 2

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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       ......`[(because 1 + tan^2theta = sec^2theta),(therefore sec^2theta - tan^2theta = 1)]`

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पाठ 6: Trigonometry - Q.1 (B)

संबंधित प्रश्‍न

Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.


Prove the following trigonometric identities.

`sin^2 A + 1/(1 + tan^2 A) = 1`


Prove the following trigonometric identities.

`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`


Prove the following identities:

`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`


Prove the following identities:

`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`


Prove the following identities:

`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`


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


`cos^2 theta + 1/((1+ cot^2 theta )) =1`

     


Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`


Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:

sin θ × cosec θ = ______


Prove the following identity : 

`sqrt(cosec^2q - 1) = "cosq  cosecq"`


prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`


Without using trigonometric identity , show that :

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


Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.


Choose the correct alternative:

sec2θ – tan2θ =?


Choose the correct alternative:

tan (90 – θ) = ?


If tan θ + cot θ = 2, then tan2θ + cot2θ = ?


If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ


`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.


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