Advertisements
Advertisements
Question
Prove the following trigonometric identities.
`(cot A + tan B)/(cot B + tan A) = cot A tan B`
Advertisements
Solution
We have to prove `(cot A + tan B)/(cot B + tan A) = cot A tan B`
Now
`(cot A + tan B)/(cot B + tan A) = (cot A + 1/cot B)/(cot B + 1/cot A)`
`= ((cot A cot B + 1)/cot B)/((cot A cot B +1)/cot A)`
`= cot A/cot B`
`= cot A 1/cot B`
= cot A tan B
Hence proved
APPEARS IN
RELATED QUESTIONS
Write the value of `(1 + cot^2 theta ) sin^2 theta`.
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
Write the value of tan1° tan 2° ........ tan 89° .
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Prove that `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.
If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`
If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1
Choose the correct alternative:
1 + cot2θ = ?
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
If tan θ = `13/12`, then cot θ = ?
If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
