Question

Prove that :
sinA(1+tanA) + cosA(1+cotA) = secA + cosecA​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

sinA(1+tanA)+cosA(1+cotA)

=sinA+sinAtanA+cosA+cosAcotA

=sinA+sinA

cosA

sinA

+cosA+cosA

sinA

cosA

[∵tanA=

cosA

sinA

,cotA=

sinA

cosA

]

=sinA+

cosA

sin

2

A

+cosA+

sinA

cos

2

A

=

sinAcosA

sin

2

Acos+sin

3

A+cos

2

AsinA+cos

3

A

=

sinAcosA

sinAcosA(sinA+cosA)sin

3

A+cos

3

A

=

sinAcosA

sinAcosA(sinA+cosA)(sin

2

A+cos

2

A−cosAsinA)

[∵a

3

+b

3−(a+b)(a

2

−ab+b

2

)

]

=

sinacosA

(sinA+cosA)sinAcosA+sin

2

A+cos

2

A−sina+cosA

=

sinacosA

(sinA+cosA).1

[∵sin²A + cos²A = 1 ]

sinAcosA

sinA

+

sinAcosA

cosA

=

1/CosA

+

1/sinA

=secA+cosec A