Math, asked by kishan8670, 11 months ago

Tan 70-Tan 20 =2 Tan 50

Answers

Answered by siddddd25

2

Answer:

Step-by-step explanation:

consider Left hand side:

tan70 = sin70/cos70

tan20 = sin20/cos20

sin70/cos70 - sin20/cos20

taking LCM:

(sin70cos20 - sin20cos70)/cos70cos20

(SINCE: sinAcosB-sinBcosA=sin(A-B)

sin(70-20)/cos70cos20 = sin50/cos70cos20

NOW :

cos70 = sin20 (SINCE: cos(90-70) = sin20)

sin50/sin20cos20

MULTIPLY AND DIVIDE BY 2:

2sin50/2sin20cos20

(SINCE: 2sinacosa = sin2a):

2sin50/sin2*20

2sin50/sin40

(SINCE: sin40 = cos50):

2sin50/cos50

= 2tan50

As LHS = RHS

hence proved

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