Question

2. In the equation tan 70 = cot (50-30°), if both the angles are acute angles, find
value of 0​

Answer 1

QUESTION:

If tan 7theta = cot(5 theta – 30°), both angles being acute angles, find the value of theta.

(correct question)

ANSWER:

We use the trigonometry identity here;

either

\tan( \alpha ) = \cot(90 - \alpha )tan(α)=cot(90−α)

or

\cot( \alpha ) = \tan(90 - \alpha )cot(α)=tan(90−α)

now come to main question ;

I LET THETHA AS ALPHA.

\tan(7 \alpha ) = \cot(5 \alpha - 30)tan(7α)=cot(5α−30)

\cot(90 - 7 \alpha ) = \cot( 5\alpha - 30)cot(90−7α)=cot(5α−30)

cot will cancel out.

\begin{gathered}90 - 7 \alpha = 5 \alpha - 30 \\ 90 + 30 = 5 \alpha + 7 \alpha \\ 120 = 12 \alpha \\ \frac{120}{12} = \alpha \\ 10 = \alpha \end{gathered}90−7α=5α−3090+30=5α+7α120=12α12120=α10=α

FINAL ANSWER :

value of thetha is 10°.

Answer 2

$\huge\purple{\mathbb{Given}}$

In the equation tan 70 = cot (50-30°), if both the angles are acute angles.

$\huge\purple{\mathbb{To find }}$

find value of θ.

$\huge\purple{\mathbb{Prove ☟︎︎︎}}$

tan 7 theta = cot (5theta – 30 degree)

cot (90 - 7θ) = cot (5θ - 30)

90 - 7θ = 5θ - 30 cot (90 - θ) = tan θ

120 = 12θ

θ = 10

therefore, the value of θ is 10.