Advertisements
Advertisements
प्रश्न
Prove that `"cosec" θ xx sqrt(1 - cos^2theta)` = 1
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
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Prove the following trigonometric identities.
`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta)/cos theta`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
`(sec^2 theta -1)(cosec^2 theta - 1)=1`
`sqrt((1+sin theta)/(1-sin theta)) = (sec theta + tan theta)`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
If `secθ = 25/7 ` then find tanθ.
Write the value of sin A cos (90° − A) + cos A sin (90° − A).
The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`cos 63^circ sec(90^circ - θ) = 1`
Evaluate:
`(tan 65^circ)/(cot 25^circ)`
Prove that: `1/(sec θ - tan θ) = sec θ + tan θ`.
Prove that `(1 + sintheta)/(1 - sin theta)` = (sec θ + tan θ)2
Let α, β be such that π < α – β < 3π. If sin α + sin β = `-21/65` and cos α + cos β = `-27/65`, then the value of `cos (α - β)/2` is ______.
