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

2 thoughts on “2. In the equation tan 70 = cot (50-30°), if both the angles are acute angles, find<br />value of 0​”

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°.

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2. [tex]\huge\purple{\mathbb{Given}}[/tex]

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

   [tex]\huge\purple{\mathbb{To find }}[/tex]

   find value of θ.

   [tex]\huge\purple{\mathbb{Prove ☟︎︎︎}}[/tex]

   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.

   Reply