Advertisements
Advertisements
Question
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
Advertisements
Solution
L.H.S = `(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
= `((sin "A" - sin "B")(sin "A" + sin "B") + (cos "A" - cos "B")(cos"A" + cos "B"))/((cos"A" + cos "B")(sin"A" + sin "B"))`
= `(sin^2"A" - sin^2"B" + cos^2"A" - cos^2"B")/((cos"A" + cos"B")(sin"A" + sin"B"))`
= `((sin^2"A" + cos^2"A") - (sin^2"B" + cos^2"B"))/((cos"A" + cos"B")(sin"A" + sin"B"))`
= `(1 - 1)/((cos"A" + cos"B")(sin"A" + sin"B")) = 0/((cos"A" + cos"B")(sin"A" + sin"B"))`
= 0
L.H.S = R.H.S ⇒ `(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")` = 0
APPEARS IN
RELATED QUESTIONS
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Prove that:
`(tanA + 1/cosA)^2 + (tanA - 1/cosA)^2 = 2((1 + sin^2A)/(1 - sin^2A))`
If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x2 + y2 + z2 = r2
Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`
The value of sin2 29° + sin2 61° is
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove the following identity:
tan2A − sin2A = tan2A · sin2A
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
If `sec θ + tan θ = sqrt(3)`, complete the activity to find the value of sec θ – tan θ.
Activity:
`square = 1 + tan^2θ` ...[Fundamental trigonometric identity]
`square - tan^2θ = 1`
`(sec θ + tan θ) . (sec θ - tan θ) = square`
`sqrt(3) . (sec θ - tan θ) = 1`
`(sec θ - tan θ) = square`
Prove that `(1 + sin B)/(cos B) + (cos B)/(1 + sin B) = 2 sec B`.
