Advertisements
Advertisements
प्रश्न
Prove that:
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1
Advertisements
उत्तर
Taking LHS
(cosec θ - sinθ )(secθ - cos θ ) ( tanθ +cot θ)
`(1/(sin theta )- sin theta )(1/(cos θ )- cosθ )((sin θ)/(cos θ) +(cos θ)/(sin θ))`
`=((1-sin^2 θ)/(sin θ)) ((1- cos ^2θ)/(cos θ)) ((sin^2 θ + cos^2 θ)/(sin θ . cos θ))`
`= (cos^2 θ)/( sin θ) xx (sin^2 θ)/(cos θ ) xx 1/(sinθ . cos θ )` = 1 = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
Prove the following identities:
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
If `( tan theta + sin theta ) = m and ( tan theta - sin theta ) = n " prove that "(m^2-n^2)^2 = 16 mn .`
Prove the following identity :
`(1 - tanA)^2 + (1 + tanA)^2 = 2sec^2A`
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
`5/(sin^2θ) - 5cot^2θ`, complete the activity given below.
Activity:
`5/(sin^2θ) - 5cot^2θ`
= `square (1/(sin^2θ) - cot^2θ)`
= `5(square - cot^2θ) ...[1/(sin^2θ) = square]`
= 5(1)
= `square`
Eliminate θ if x = r cosθ and y = r sinθ.
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
