Question

Express the trigonometric ratios sinA, SecA and tanA in terms of cotA

Answer 1

Hola!

[ i ] sinA in terms of cotA :

sinA = 1 / cosecA

We know that: cosec²A = 1 + cot²A

sinA = 1 / √1 + cot²A

[ ii ] secA in terms of cotA :

We know that: 1 + tan²A = sec²A

secA = 1 + tan²A

secA = 1 + 1 / cot²A

secA = √(cot²A + 1 ) /cotA

[ iii ] tanA in terms of cotA :

tanA = 1 / cotA

Hope it helps! :D

Answer 2

hello friend...!!!

according to the given question we should convert the ratios of sinA, sec A and tan A in terms of cot A


now, we know that,

tan A = 1 / Cot A

also, secA = 1 + tan^2 A

therefore,

sec A = 1 + 1/ cot ^2 A

sec A = ( cot ^2 A + 1 ) / cot ^2 A.

we know that,

cos A = 1 / sec A

therefore,

Cos A in terms of Cot A is,

Cos A = Cot ^2 A /( Cot ^2 A + 1 )

similarly,

sin A = Cos A / cot A

therefore,

Sin A = cot ^2A / ( Cot ^2 A + 1 ) Cot A

therefore,

Sin A = Cot A / ( Cot ^2 A + 1 )


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hope it helps...!!!!