Attempt this Trigonometry Practice Question

Question of The Day05-07-2021

If (α – β) = 60⁰ and tan α * cot β = 4, then find the value of sin (α + β).

Answer

Correct Answer : b ) \({7 \sqrt 3} \over 6\)

Explanation :

According to the question

tanα * cotβ = 4

we know that

\(tanθ\)=\({sinθ \over cosθ} and \ cotθ={cosθ \over sinθ}\)

⇒\({sin \ α \over cos\ α}*{cos \ β \over sin\ β}\)=4

Using componendo and dividendo

⇒\({sin\ α \ cos\ β+cos\ α \ sin\ β} \over {sin \ α \ cos\ β-cos\ α \ sin\ β}\)=\({4+1 } \over {4-1}\)

⇒\(sin (α+β) \over sin(α-β)\)=\(5 \over 3\)

⇒ 3 sin (α + β) = 5 sin (α - β)

Substituting the value of (α - β) = 60⁰

⇒ 3 sin (α + β) = 5 * sin (60⁰)

⇒3 sin (α+β)=\({ 5* \sqrt3 } \over 2\)

⇒sin (α+β)=\({ 5 \sqrt3 } \over 6\)

Hence, (a) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc.

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