Question

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solve the question of trigonometry proving its question number 5 try to solve it from lhs left hand side

Answer 1

Answer:

To Prove (sin A - cos A)(1+tan A+cot A) = [(sec A/cosec² A) - (cosec A/sec² A)]

Step-by-step explanation:

Take LHS,

(sin A - cos A)(1+tan A+cot A)

= sin A + sin A.tan A + sin A.cot A - cos A - cos A.tan A - cos A.cot A

= sin A + sin A*(sin A/cos A) + sin A*(cos A/sin A) - cos A - cos A(sin A/cos A) - cos A(cos A/sin A)

=sin A + (sin² A/cos A) + cos A -cos A - sin A - (cos² A/sin A)

= (sin² A/cos A) - (cos² A/sin A)

= [(1/cosec² A)*(1/cos A)] - [(1/sec² A)*(1/sin A)]

=[(1/cosec² A)*sec A] - [(1/sec² A)*cosec A]

= [(sec A /cosec² A) - (cosec A/sec² A)]

= RHS

Hence Proved