Advertisements
Advertisements
рдкреНрд░рд╢реНрди
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
рдЙрддреНрддрд░
LHS = `(tan A + tanB )/(cot A + cot B) `
=`(tan A + tan B)/(1/ tan A + 1/ tanB)`
=` (tan A + tan B)/( (tan A+tan B)/ (tan A tan B)`
=`(tan A tan B ( tan A + tan B))/((tan A + tan B ))`
= ЁЭСбЁЭСОЁЭСЫЁЭР┤ ЁЭСбЁЭСОЁЭСЫЁЭР╡
= RHS
Hence, LHS = RHS
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
`(1 + cot^2 theta ) sin^2 theta =1`
`sqrt((1+sin theta)/(1-sin theta)) = (sec theta + tan theta)`
Write the value of cos1° cos 2°........cos180° .
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
If cos A + cos2 A = 1, then sin2 A + sin4 A =
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Prove that sin θ sin( 90° - θ) - cos θ cos( 90° - θ) = 0
Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot θ)`
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
Prove that `sec"A"/(tan "A" + cot "A")` = sin A
Prove the following that:
`tan^3θ/(1 + tan^2θ) + cot^3θ/(1 + cot^2θ)` = secθ cosecθ – 2 sinθ cosθ