Sir in one of your videos it was given that tan A- A-2 cosec 2 AAndA-tan A-2 2 ASir could you please prove these 2 identities i am unable to prove- Thank you sir-

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

Sir in one of...

Question

Sir in one of your videos it was given that

tanA+cotA=2cosec2A

And

cot A - tanA=2cot2A

Sir could you please prove these 2 identities i am unable to prove.

Thank you sir.

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Solution

tanA + cotA = (sinA/cosA) + (cosA/sinA)
. . . . . . . . . = (sinA.sinA + cosA.cosA)/sinA.cosA
. . . . . . . . . = 2 (sin²A + cos²A) / 2 sinA.cosA
. . . . . . . . . = 2 × 1/sin2A
. . . . . . . . . = 2 cosec2A

LH.S. = cotA - tanA = cosA/sinA - sinA/cosA
L.H.S. = [(cosA)^2 - (sinA)^2] / sinA.cosA
L.H.S. = 2.cos2A / 2sinA.cosA
L.H.S. = 2.cos2A / sin2A

L.H.S. = 2.cot2A = R.H.S.

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Sir in one of your videos it was given that tanA+cotA=2cosec2A And cot A - tanA=2cot2A Sir could you please prove these 2 identities i am unable to prove. Thank you sir.

Sir in one of your videos it was given that

tanA+cotA=2cosec2A

And

cot A - tanA=2cot2A

Sir could you please prove these 2 identities i am unable to prove.

Thank you sir.