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

Choose the correct alternative: cot θ . tan θ = ? - Geometry Mathematics 2

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प्रश्न

Choose the correct alternative:

cot θ . tan θ = ?

पर्याय

  • 1

  • 0

  • 2

  • `sqrt(2)`

MCQ

उत्तर

1

cot θ. tan θ = `1/"tan θ"`. tan θ = 1.

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पाठ 6: Trigonometry - Q.1 (A)

संबंधित प्रश्‍न

Prove the following trigonometric identities.

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


Prove the following trigonometric identities.

if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`


Prove the following trigonometric identities.

if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1


If cos θ + cos2 θ = 1, prove that sin12 θ + 3 sin10 θ + 3 sin8 θ + sin6 θ + 2 sin4 θ + 2 sin2 θ − 2 = 1


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


Simplify 

sin A `[[sinA   -cosA],["cos A"  " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`


Prove the following identity : 

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


Without using trigonometric identity , show that :

`sin(50^circ + θ) - cos(40^circ - θ) = 0`


If sin θ = `1/2`, then find the value of θ. 


Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.


If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.


Prove that `(tan θ)/(cot(90° - θ)) + (sec (90° - θ) sin (90° - θ))/(cosθ. cosec θ) = 2`.


Prove the following identities.

`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ


Prove the following identities.

`costheta/(1 + sintheta)` = sec θ – tan θ


Prove the following identities.

`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`


If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`


If sec θ = `25/7`, find the value of tan θ.

Solution:

1 + tan2 θ = sec2 θ

∴ 1 + tan2 θ = `(25/7)^square`

∴ tan2 θ = `625/49 - square`

= `(625 - 49)/49`

= `square/49`

∴ tan θ = `square/7` ........(by taking square roots)


If tan θ × A = sin θ, then A = ?


If cosec A – sin A = p and sec A – cos A = q, then prove that `("p"^2"q")^(2/3) + ("pq"^2)^(2/3)` = 1


If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`


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