Question

if tan A=1 ,find the value of sinA cosA
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Answer 1

It is given that the numeric value of tanA is 1 . And, we know that tane is the ratio of sine and cosine of the same angle.

Thus,

= > tanA = 1

= > sinA / cosA = 1

= > sinA = cosA -----: ( 1 )

Also, from the properties of trigonometry :

• sinA = 1 / cosecA

• cosA = 1 / secA

= > 1 / cosecA = 1 / secA

= > secA = cosecA ----: ( 2 )

Therefore,

= > ( sinA + cosA ) / ( secA + cosecA )

From ( 1 ) , sinA = cosA

From ( 2 ), secA = cosecA

So,

= > ( sinA + sinA ) / ( cosecA + cosecA )

= > 2 sinA / 2 cosecA

= > sinA / cosecA

= > sinA / ( 1 / sinA )

= > sin²A

And, tanA = 1 = > tanA = tan45° = > A = 45°

= > sin² 45°

= > ( 1 / √2 )²

= > 1 / 2

Hence the numeric value of sinA + cosA / secA + cosecA is 1 / 2.