Advertisements
Advertisements
Question
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
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 the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
`(1+ cos theta + sin theta)/( 1+ cos theta - sin theta )= (1+ sin theta )/(cos theta)`
The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
If cosθ = `5/13`, then find sinθ.
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
Prove that sin6A + cos6A = 1 – 3sin2A . cos2A
If 2sin2β − cos2β = 2, then β is ______.
Show that `(cos^2(45^circ + theta) + cos^2(45^circ - theta))/(tan(60^circ + theta) tan(30^circ - theta))` = 1
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
