Advertisements
Advertisements
प्रश्न
Prove that:
(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1
Advertisements
उत्तर
(tan A + cot A) (cosec A – sin A) (sec A – cos A)
= `(sinA/cosA + cosA/sinA)(1/sinA - sinA)(1/cosA - cosA)`
= `((sin^2A + cos^2A)/(sinAcosA))((1 - sin^2A)/sinA)((1 - cos^2A)/cosA)`
= `(1/(sinAcosA))(cos^2A/sinA)(sin^2A/cosA)`
= 1
संबंधित प्रश्न
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`
If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`
What is the value of 9cot2 θ − 9cosec2 θ?
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
Prove the following identity :
`(1 + cotA + tanA)(sinA - cosA) = secA/(cosec^2A) - (cosecA)/sec^2A`
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Find the value of ( sin2 33° + sin2 57°).
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
Prove that
`(cot "A" + "cosec A" - 1)/(cot"A" - "cosec A" + 1) = (1 + cos "A")/"sin A"`
