Advertisements
Advertisements
प्रश्न
Prove that `"cosec" θ xx sqrt(1 - cos^2theta)` = 1
Advertisements
उत्तर
L.H.S = `"cosec" θ xx sqrt(1 - cos^2theta)`
= `"cosec" θ xx sqrt(sin^2theta)` ......`[(because sin^2theta + cos^2theta = 1),(therefore 1 - cos^2theta = sin^2theta)]`
= cosec θ × sin θ
= 1 ......[∵ sin θ × cosec θ = 1]
= R.H.S
APPEARS IN
संबंधित प्रश्न
If `sec alpha=2/sqrt3` , then find the value of `(1-cosecalpha)/(1+cosecalpha)` where α is in IV quadrant.
Prove the following trigonometric identities.
`tan theta + 1/tan theta = sec theta cosec theta`
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\]
Write True' or False' and justify your answer the following:
\[ \cos \theta = \frac{a^2 + b^2}{2ab}\]where a and b are two distinct numbers such that ab > 0.
sec4 A − sec2 A is equal to
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/2`
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
Prove that tan2Φ + cot2Φ + 2 = sec2Φ.cosec2Φ.
Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = cosec θ - cot θ`.
Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.
If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
Prove that (1 – cos2A) . sec2B + tan2B(1 – sin2A) = sin2A + tan2B
sin(45° + θ) – cos(45° – θ) is equal to ______.
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
