Question

if cot a=3/4,then find the value of sin a+ cosa,sin a= cos a answer​

Answer 1

Correct Statement is

$\tt \: If \: cota =\dfrac{3}{4}, \: find \: value \: of \: \dfrac{sina + cosa}{sina - cosa}$

$\large\underline{\bold{Solution-}}$

Given that

$\rm :\longmapsto\:cota = \dfrac{3}{4}$

Now,

• Consider,

$\rm :\longmapsto\:\dfrac{sina + cosa}{sina - cosa}$

On dividing numerator and denominator by sina, we get

$\rm :\longmapsto\:\dfrac{\dfrac{sina}{sina} + \dfrac{cosa}{sina} }{\dfrac{sina}{sina} - \dfrac{cosa}{sina} }$

$\rm :\longmapsto\:\dfrac{1 + cota}{1 -cota }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \because \bf \: \dfrac{cosa}{sina} = cota} \:$

$\rm :\longmapsto\:\dfrac{1 + \dfrac{3}{4} }{1 - \dfrac{3}{4} }$

$\rm :\longmapsto\:\dfrac{4 + 3}{4 - 3}$

$\rm :\longmapsto\:7$

So,

• The value of

$\boxed{\bf :\implies\:\dfrac{sina + cosa}{sina - cosa} = 7 \: \: \: when \: cota = \dfrac{3}{4} }$

Additional Information:-

Additional Information:- Relationship between sides and T ratios

sin θ = Opposite Side/Hypotenuse

cos θ = Adjacent Side/Hypotenuse

tan θ = Opposite Side/Adjacent Side

sec θ = Hypotenuse/Adjacent Side

cosec θ = Hypotenuse/Opposite Side

cot θ = Adjacent Side/Opposite Side

Reciprocal Identities

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

sin θ = 1/cosec θ

cos θ = 1/sec θ

tan θ = 1/cot θ

Co-function Identities

sin (90°−x) = cos x

cos (90°−x) = sin x

tan (90°−x) = cot x

cot (90°−x) = tan x

sec (90°−x) = cosec x

cosec (90°−x) = sec x

Fundamental Trigonometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

cosec²θ - cot²θ = 1