If cosec -54- then find the value of 1-tan- 1-tan- 1- 1-

We know that, ^2θ= cosec^2θ 1=[54 nbsp; ]^2 1 =2516 1 ⇒^2θ=25 1616 ⇒^2θ=916 ⇒θ=34= ⇒tanθ=43 ( 1+tanθ)( 1 tanθ)( 1+θ)( 1 θ) = [ 1+43][ 1 43][ nbsp; 1+34] ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Properties of Cube Root of a Complex Number

If cosec θ=54...

Question

If $c o s e c θ = \frac{5}{4}$ , then find the value of $\frac{(1 + tan θ) (1 - tan θ)}{(1 + cot θ) (1 - cot θ)}$

Open in App

Solution

We know that, ${cot}^{2} θ = c o s e c^{2} θ - 1 = {[\frac{5}{4}]}^{2} - 1 = \frac{25}{16} - 1$

$\Rightarrow {cot}^{2} θ = \frac{25 - 16}{16}$

$\Rightarrow {cot}^{2} θ = \frac{9}{16}$

$\Rightarrow cot θ = \frac{3}{4} =\Rightarrow tan θ = \frac{4}{3}$

$\frac{(1 + tan θ) (1 - tan θ)}{(1 + cot θ) (1 - cot θ)} = \frac{[1 + \frac{4}{3}] [1 - \frac{4}{3}]}{[1 + \frac{3}{4}] [1 - \frac{3}{4}]} = \frac{[\frac{7}{3}] [\frac{- 1}{3}]}{[\frac{7}{4}] [\frac{1}{4}]} = \frac{\frac{- 7}{9}}{\frac{7}{16}} = \frac{- 16}{9}$

Suggest Corrections

Similar questions

Q. The value of

(1 + tan θ + sec θ) (1 + cot θ - cosec θ)

is:

Q. check if

\frac{tan θ}{1 - cot θ} + \frac{cot θ}{1 - tan θ} = 1 + sec θ csc θ

\frac{tanθ}{(1 - cotθ)} + \frac{cotθ}{(1 - tanθ)} = (1 + secθ cosecθ)

$(1 + t a n θ + s e c θ) (1 + c o t θ - c o s e c θ)$

Show that $\frac{tan θ}{(1 - cot θ)} + \frac{cot θ}{(1 - tan θ)} = (1 + sec θ cosec θ)$

Join BYJU'S Learning Program

If cosecθ=54, then find the value of (1+tanθ)(1−tanθ)(1+cotθ)(1−cotθ)

We know that, cot2θ= cosec2θ−1=[54]2−1=2516−1 ⇒cot2θ=25−1616 ⇒cot2θ=916 ⇒cotθ=34=⇒tanθ=43 (1+tanθ)(1−tanθ)(1+cotθ)(1−cotθ)=[1+43][1−43][1+34][1−34]=[73][−13][74][14]=−79716=−169

If $c o s e c θ = \frac{5}{4}$ , then find the value of $\frac{(1 + tan θ) (1 - tan θ)}{(1 + cot θ) (1 - cot θ)}$