Question : If $21 an heta=20$, then $(1+\sin heta+\cos heta):(1-\sin heta+\cos heta)=$?
Option 1: 5 : 2
Option 2: 3 : 1
Option 3: 7 : 3
Option 4: 2 : 1

Question

Question : If $21 an heta=20$, then $(1+\sin heta+\cos heta):(1-\sin heta+\cos heta)=$?

Option 1: 5 : 2

Option 2: 3 : 1

Option 3: 7 : 3

Option 4: 2 : 1

Team Careers360 · Accepted Answer

Correct Answer: 7 : 3

Solution : Given: $21 an heta=20$
⇒ $ an heta = \frac{20}{21}=\frac{ ext{Perpendicular}}{ ext{Base}}$
Let the perpendicular and the base be 20 units and 21 units respectively.
Use the formulas,
$ an heta=\frac{ ext{Perpendicular}}{ ext{Base}}$,
$\sin heta=\frac{ ext{Perpendicular}}{ ext{Hypotenuse}}$,
$\cos heta=\frac{ ext{Base}}{ ext{Hypotenuse}}$,
Pythagoras's theorem: $ ext{Hypotenuse}^2= ext{Base}^2+ ext{Perpendicular}^2$
⇒ $ ext{Hypotenuse}^2={21}^2+{20}^2$
⇒ $ ext{Hypotenuse}^2=441+400$
⇒ $ ext{Hypotenuse}^2=841$
⇒ $ ext{Hypotenuse}=\sqrt{841}$
⇒ $ ext{Hypotenuse}=29$
The value of $(1+\sin heta+\cos heta):(1-\sin heta+\cos heta)$ is given as,
$=(1+\frac{20}{29}+\frac{21}{29}):(1-\frac{20}{29}+\frac{21}{29})$
$=\frac{29+20+21}{29}:\frac{29–20+21}{29}$
$=\frac{70}{29}:\frac{30}{29}=7:3$
Hence, the correct answer is 7 : 3.

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Question : If 21tan⁡θ=20, then (1+sin⁡θ+cos⁡θ):(1−sin⁡θ+cos⁡θ)=?Option 1: 5 : 2Option 2: 3 : 1Option 3: 7 : 3Option 4: 2 : 1

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Question : If $21 \tan θ = 20$ , then $(1 + \sin θ + \cos θ) : (1 - \sin θ + \cos θ) =$ ?
Option 1: 5 : 2
Option 2: 3 : 1
Option 3: 7 : 3
Option 4: 2 : 1