If tan =7/4 then cot a is
Answers
Answer:
4/7 is right answer because cot is reciprocal of tan
Answer:
If (tan theta + cot theta ) = 7/4 then (tan^2 theta +cot^2 theta) = \dfrac{17}{16}
16
17
Step-by-step explanation:
⁸Given tan\theta +cot\theta =\dfrac{7}{4}tanθ+cotθ=
4
7
We have to find tan^{2}\theta +cot^{2}\thetatan
2
θ+cot
2
θ
We know the identity ( \textrm{a+b} )^{2}=\textrm{a}^{2}+\textrm{b}^{2}+2\textrm{ab}(a+b)
2
=a
2
+b
2
+2ab
So we have
(tan\theta +cot\theta )^{2}=tan^{2}\theta +cot^{2} \theta +2tan\theta cot\theta(tanθ+cotθ)
2
=tan
2
θ+cot
2
θ+2tanθcotθ
\Rightarrow tan^{2}\theta +cot^{2} \theta = (tan\theta +cot\theta )^{2}-2tan\theta cot\theta⇒tan
2
θ+cot
2
θ=(tanθ+cotθ)
2
−2tanθcotθ
\Rightarrow tan^{2}\theta +cot^{2} \theta = (\dfrac{7}{4} )^{2}-2tan\theta \times\frac{1}{tan\theta }⇒tan
2
θ+cot
2
θ=(
4
7
)
2
−2tanθ×
tanθ
1
\Rightarrow tan^{2}\theta +cot^{2} \theta = (\dfrac{7}{4} )^{2}-2⇒tan
2
θ+cot
2
θ=(
4
7
)
2
−2
\Rightarrow tan^{2}\theta +cot^{2} \theta =\dfrac{49}{16}-2⇒tan
2
θ+cot
2
θ=
16
49
−2
\Rightarrow tan^{2}\theta +cot^{2} \theta =\dfrac{49-32}{16}⇒tan
2
θ+cot
2
θ=
16
49−32
\Rightarrow tan^{2}\theta +cot^{2} \theta =\dfrac{17}{16}⇒tan
2
θ+cot
2
θ=
16
17
May this help u plzz mark me as brainliest