Advertisements
Advertisements
प्रश्न
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
Advertisements
उत्तर
L.H.S. = `tanA/(1 - cotA) + cotA/(1 - tanA)`
= `tanA/(1 - 1/tanA) + (1/tanA)/(1 - tanA)`
= `tan^2A/(tanA - 1) + 1/(tanA(1 - tanA))`
= `(tan^3A - 1)/(tanA(1 - tanA))`
= `((tanA - 1)(tan^2A + 1 + tanA))/(tanA(tanA - 1)`
= `(sec^2A + tanA)/tanA`
= `(1/cos^2A)/(sinA/cosA) + 1`
= `1/(sinAcosA) + 1`
= sec A cosec A + 1 = R.H.S.
APPEARS IN
संबंधित प्रश्न
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
If tan A = n tan B and sin A = m sin B , prove that `cos^2 A = ((m^2-1))/((n^2 - 1))`
Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`.
Prove the following identity :
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Without using trigonometric identity , show that :
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
Prove that `"cosec" θ xx sqrt(1 - cos^2θ) = 1`.
The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.
