Question

prove that 1 / tan A +cot A = cos A sinA
​

Answer 1

MATHS

Prove that :

(1+cotA+tanA)(sinA−cosA)=sinAtanA−cotAcosA.

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ANSWER

Let

L.H.S= (1+cotA+tanA)(sinA−cosA)

=(1+

sinA

cosA

+

cosA

sinA

)(sinA−cosA)

=(

sinAcosA

sinAcosA+cos

2

A+sin

2

A

)(sinA−cosA)

=(1+sinAcosA)(

sinAcosA

sinA−cosA

)

Now,

R.H.S=sinAtanA−cotAcosA

=sinA

cosA

sinA

−

sinA

cosA

cosA

=

cosA

sin

2

A

−

sinA

cos

2

A

=

sinAcosA

sin

3

A−cos

3

A

=

sinAcosA

(sinA−cosA)

(sin

2

A+cos

2

A+sinAcosA)

=(1+sinAcosA)

sinAcosA

(sinA−cosA)

Hence,

L.H.S=R.H.S

proved

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