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Visualisation of Trigonometric Ratios Using a Unit Circle

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Question

prove that ( 1 + cot a - cosec a ) ( 1 + tan a + sec a) = 2

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Solution

(1 + cot A - cosec A ) (1 + tan A + sec A ) = 2

L.H.S. = (1 + cos A/sin A - 1/sin A ) (1 + sin A/cos A + 1 / cos A ) { CONVERTING }

L.H.S. = (sin A + cos A - 1 / sin A ) (cos A + sin A +1 / cos A )

L.H.S. = (sin A + cos A )² - (1)² / sin Acos A { MULTIPLYING USING IDENTITY }

L.H.S. = (sin²A + cos²A) + 2sin Acos A - 1 / sin Acos A

L.H.S. = 1 + 2sin Acos A -1 / sin Acos A

L.H.S. = 2sin Acos A / sin Acos A

L.H.S. = 2

Hence, L.H.S = R.H.S

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Similar questions

Q. Prove the following trigonometric identities.

(1 + cot A − cosec A) (1 + tan A + sec A) = 2

Prove the following identities:

$(s e c A - c o s e c A) (1 + t a n A + c o t A) = t a n A s e c A - c o t A c o s e c A$

Q. Prove the following trigonometric identities.

(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A

(1 + c o t A - c o s e c A) (1 + t a n A + s e c A) = 2

Q. The value of

(1 + cot A - cosec A) (1 + tan A + sec A)

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