Advertisements
Advertisements
प्रश्न
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
Advertisements
उत्तर
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
संबंधित प्रश्न
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
if `cosec theta - sin theta = a^3`, `sec theta - cos theta = b^3` prove that `a^2 b^2 (a^2 + b^2) = 1`
Show that : tan 10° tan 15° tan 75° tan 80° = 1
Write the value of cos1° cos 2°........cos180° .
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove the following identities:
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Prove that
`(cot "A" + "cosec A" - 1)/(cot"A" - "cosec A" + 1) = (1 + cos "A")/"sin A"`
