Advertisements
Advertisements
प्रश्न
Prove that `(cot "A" + "cosec A" - 1)/(cot "A" - "cosec A" + 1) = (1 + cos "A")/sin "A"`
Advertisements
उत्तर
LHS = `(cot "A" + "cosec A" - 1)/(cot "A" - "cosec A" + 1)`
= `((cot "A" + "cosec A") - ("cosec"^2 "A" - cot^2 "A"))/(cot "A" - "cosec A" + 1)`
= `((cot "A" + "cosec A")("cosec A" + cot "A")("cosec A" - cot "A"))/(cot "A" - "cosec A" + 1)`
= `((cot "A" + "cosec A") [1 - "cosec A" - cot "A"])/(cot"A"-"cosec A"+1)`
= `((cot "A" + "cosec A") (1-"cosec A"+cot"A"))/(1-"cosec A"+cot"A")`
= cot A + cosec A
= `cos"A"/sin"A"+1/sin"A"=(cos"A"+1)/sin"A"`
= `(1+cos"A")/sin"A"`
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities.
`((1 + sin theta - cos theta)/(1 + sin theta + cos theta))^2 = (1 - cos theta)/(1 + cos theta)`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
Prove the following identities:
`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`
`(sec^2 theta -1)(cosec^2 theta - 1)=1`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
If `( tan theta + sin theta ) = m and ( tan theta - sin theta ) = n " prove that "(m^2-n^2)^2 = 16 mn .`
(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
For ΔABC , prove that :
`tan ((B + C)/2) = cot "A/2`
Prove that tan2Φ + cot2Φ + 2 = sec2Φ.cosec2Φ.
