Question

Sin theta+Cosec theta=2 then Sin^2 theta+Cosec^2 theta=?

Answer 1

Question :-

If sin∅ + cosec∅ = 2 , then find the value of sin²∅ + cosec²∅ .

Solution :-

sin∅ + cosec∅ = 2

• Squaring both sides .

→ (sin∅ + cosec∅)² = 2²

→ $\sf{sin^2\theta+cosec^2\theta+2sin\theta.cosec\theta=4}$

→ sin²∅ + cosec²∅ + 2×1 = 4

→ sin²∅ + cosec²∅ + 2 = 4

→ sin²∅ + cosec²∅ = 4 - 2

→ sin²∅ + cosec²∅ = 2

Therefore, the value of sin²∅ + cosec²∅ is 2.

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Some formulas :-

★ sin²A + cos²A = 1

★ 1 + tan²A = sec²A

★ 1 + cot²A = cosec²A

★ cos²A - sin²A = cos2A

★ sin (A+B) = sinAcosB + cosAsinB

★ sin (A-B) = sinAcosB - cosAsinB

★ cos(A+B) = cosAcosB - sinAsinB

★ cos(A-B) = cosAcosB + sinAsinB

★ $\sf{tan(A+B)=\dfrac{tanA+tanB}{1-tanAtanB}}$

★ $\sf{tan(A-B)=\dfrac{tanA-tanB}{1+tanAtanB}}$