Question

if cosec x + cot x = a then cos x =?​

Answer 1

Answer:

1/sin(x)+cos(x)/sin(x)=a

1+cos(x)=asin(x)

cos(x)=asin(x)-1

Answer 2

GIVEN

• Cosec x + cot x = a

Explanation:

$\\ \colon\implies{\tt{ cosec \ x + cot \ x = a }} \\ \\ \\ \colon\implies{\tt{ cosec \ x + cot \ x = \dfrac{1}{cosec \ x - cot \ x } = a }} \\ \\ \\ \colon\implies{\tt{ cosec \ x - cot \ x = \dfrac{1}{a} }} \\ \\ \\ \colon\implies{\tt{ 2cosec \ x = a + \dfrac{1}{a} = \dfrac{a+1}{a} }} \\ \\ \\ \colon\implies{\tt{ cosec \ x = \dfrac{a^2 + 1}{2a} }} \\ \\ \\ \colon\implies{\tt{ sin \ x = \dfrac{2a}{a^2+1} }} \\ \\ \\ \colon\implies{\tt{ cos \ x = \sqrt{ 1 - sin^2x } }} \\ \\ \\ \colon\implies{\tt{ \sqrt{ 1 - \left( \dfrac{2a}{a^2-1} \right)^2 } }} \\ \\ \\ \colon\implies{\tt{ \sqrt{ 1- \dfrac{4a^2}{(a^2+1)^2 } } }} \\ \\ \\ \colon\implies{\tt{ \sqrt{ \dfrac{(a^2+1)^2 - 4a^2}{(a^2+1)^2 } } }} \\ \\ \\ \colon\implies{\tt{ \sqrt{ \dfrac{(a^2-1)^2}{a^2+1)^2} } }} \\ \\ \\ \colon\implies{\boxed{\tt\pink{ \dfrac{a^2-1}{a^2 + 1 } }}}$

Hence,

• The Value of cos x is (a²-1)/(a²+1) .

More to Know

• sin $\theta$ = 1/cosec$\theta$
• tan $\theta$ = 1/cot$\theta$
• cot $\theta$ = cos $\theta$/sin $\theta$
• cos $\theta$ = 1/sec $\theta$
• tan $\theta$ = sin$\theta$/cos $\theta$