Question

Find the value of tan (cosec⁻¹ $\frac{65}{63}$)

Answer 1

Answer:

The answer is

tan (cosec⁻¹ 65/63) = 3.94

Explanation:

Given that

tan (cosec⁻¹ 65/63)

 ∵  cosec⁻¹ 65/63 = sin⁻¹ 63/65

     cosec⁻¹ 65/63 = sin⁻¹ 0.9692

                    ∵ We know that   y = sin x  ⇔ x ∈ [ -π/2 , π/2 ]

     cosec⁻¹ 65/63 = 75.75

So

tan (cosec⁻¹ 65/63) = tan 75.75 = 3.94

The answer is

tan (cosec⁻¹ 65/63) = 3.94

Answer 2

Answer:

$tan(cosec^{-1}\frac{65}{63})=\frac{63}{16}$

Step-by-step explanation:

As we know that cosec⁻¹x = sin⁻¹(1/x)

so cosec⁻¹(65/63) = sin⁻¹(63/65)

$tan(sin^{-1}\frac{63}{65})$

now write  sin⁻¹x in terms of tan⁻¹ x,so that botn tan and  tan⁻¹  cancels each other

$sin^{-1}x=tan^{-1}(\frac{x\sqrt{1-x^{2} } }{1-x^{2} } )\\\\here \\\\\\sin^{-1}\frac{63}{65} =tan^{-1}(\frac{\frac{63}{65}\sqrt{1-(\frac{63}{65})^{2} } }{1-(\frac{63}{65})^{2} } )\\\\\\=tan^{-1}(\frac{\frac{63}{65}\sqrt{1-(\frac{3969}{4225}) } }{1-(\frac{3969}{4225}) } )\\\\\\=tan^{-1}(\frac{\frac{63}{65}\sqrt{(\frac{4225-3969}{4225}) } }{(\frac{4225-3969}{4225}) } )\\\\\\=tan^{-1}(\frac{63}{16})\\ \\so\\\\=> tan(tan^{-1}(\frac{63}{16})\\\\\\=\frac{63}{16}$