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प्रश्न
tan θ cosec2 θ – tan θ is equal to
पर्याय
sec θ
cot2 θ
sin θ
cot θ
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उत्तर
cot θ
Explanation;
Hint:
tan θ cosec2 θ – tan θ = tan θ (cosec2 θ – 1)
= `tan theta xx cot^2 theta`
= `1/cot theta xx cot^2 theta`
= cot θ
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संबंधित प्रश्न
Prove the following trigonometric identities.
`1 + cot^2 theta/(1 + cosec theta) = cosec theta`
` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`
`(sin theta +cos theta )/(sin theta - cos theta)+(sin theta- cos theta)/(sin theta + cos theta) = 2/((sin^2 theta - cos ^2 theta)) = 2/((2 sin^2 theta -1))`
9 sec2 A − 9 tan2 A is equal to
Prove the following identity :
`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ`
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following Identities :
`(cosecA)/(cotA+tanA)=cosA`
Prove that sin( 90° - θ ) sin θ cot θ = cos2θ.
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S. = `square`
= `cos^2θ xx square` ...`[1 + tan^2θ = square]`
= `(cos θ xx square)^2`
= 12
= 1
= R.H.S.
