Question

If tan=a/b find the value of cos-sin/cos+sin.​

Answer 1

Given :-

• tan theta =a/b

To find :-

$\sf\:\:\dfrac{cos\theta -sin\theta}{cos\theta+sin\theta}$

A.T.Q :-

Divide the numerator and denominator by cos theta

$\sf\implies \dfrac{\dfrac{cos\theta}{cos\theta}-\dfrac{sin\theta}{cos\theta}}{\dfrac{cos\theta}{cos\theta}+\dfrac{sin\theta}{cos\theta}}\\ \\ \\ \sf\:\:\: we\:know\:that\:\dfrac{sin\theta}{cos\theta}=tan\theta\\ \\ \\ \sf\implies \dfrac{1-tan\theta}{1+tan\theta}\\ \\ \sf\:\:\:\:put\:the\:value\:of\: tan\theta\\ \\ \sf\implies \dfrac{1-\dfrac{a}{b}}{1+\dfrac{a}{b}}\\ \\ \\ \sf\implies \dfrac{\dfrac{b-a}{b}}{\dfrac{b+a}{b}}\\ \\ \\ \sf\implies \dfrac{b-a}{b}\times \dfrac{b}{b+a}\\ \\ \sf\implies \dfrac{b-a}{b+a}$

$\boxed{\sf{\dfrac{cos\theta-sin\theta}{cos\theta+sin\theta}=\dfrac{b-a}{b+a}}}$

Answer 2

AnswEr :

Given that,

tan∅ = a/b

To finD :

cos∅ - sin∅/cos∅ + sin∅

Now,

cos∅ - sin∅/cos∅ + sin∅

Dividing both the numerator and denominator by cos∅

→ (1 - tan∅)/(1 + tan∅)

But tan∅ = a/b

→ (1 - a/b)/(1 + a/b)

→ (b - a)/(b + a)

Thus,

cos∅ - sin∅/cos∅ + sin∅ = b - a/b + a