Advertisements
Advertisements
प्रश्न
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
Prove that: tan θ + cot θ = sec θ cosec θ
Advertisements
उत्तर
L.H.S. = cot θ + tan θ
L.H.S. = `costheta/sintheta + sintheta/costheta`
L.H.S. = `(cos^2theta + sin^2theta)/(sintheta costheta)`
[cos2 θ + sin2 θ = 1]
L.H.S. = `1/(sintheta costheta)`
Use Reciprocal Identities:
The expression can be split into `(1/sin θ) xx (1/cos θ)`.
`1/sin θ` = cosec θ
`1/cos θ` = sec θ
L.H.S. = cosec θ.sec θ
L.H.S. = sec θ.cosec θ
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove that:
(1 + tan A . tan B)2 + (tan A – tan B)2 = sec2 A sec2 B
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
Define an identity.
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
Prove the following identity :
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`(sec^2θ - sin^2θ)/tan^2θ = cosec^2θ - cos^2θ`
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/2`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
Choose the correct alternative:
1 + tan2 θ = ?
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ.
Prove that sec2θ – cos2θ = tan2θ + sin2θ.
