यदि cos (A + 31 °) = sin 47 ° है, तो sin 5A का मान क्या है ?

Question

If cos (A + 31°) = sin 47°, then what is the value of sin 5A?

A.v2(√2)

B.1/ v2(1/ √2)

C.v3/2(√3/2)

D.0(0)

Answer

C.cos (A + 31°) = sin 47° cos (A + 31°) =sin(90°-43°) (sin(90-A)=cos A) cos (A + 31°)=cos 43° A + 31°= 43° A = 12° sin 5A =sin 5 x 12°=sin 60°=√3/2 So the correct answer is option C.

C.cos (A + 31°) = sin 47° cos (A + 31°) =sin(90°- 43°) (sin(90-A)=cos A) cos (A + 31°)=cos 43° A + 31°= 43° A = 12° sin 5A =sin 5 x 12°=sin 60°=√3/2 इसलिए सही उत्तर विकल्प C है।

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Question

What is the simplified value of (Cosec^4 A - cot^2 A) - (cot^4 A + cosec^2 A)?

(Cosec^4 A - cot^2 A) - (cot^4 A + cosec^2 A) का सरलीकृत मान क्या है?

A.0(0)

B.5(5)

C.6(6)

D.9(9)

Answer

A.(Cosec^4 A - cot^2 A) - (cot^4 A + cosec^2 A) As we know [1 + cot^2A = cosec^2A] [cosec^4A = (1 + cot^2A)^2=1 + cot^4A + 2 cot^2A] =cosec^4A – cot^4A – cot^2A – cosec^2A =1 + cot^4A + 2 cot^2A – cot^4A – cot^2A – cosec^2A = 1 + cot^2A – cosec^2A = cosec^2A - cosec^2A = 0 So the correct answer is option A.

A.(Cosec^4 A - cot^2 A) - (cot^4 A + cosec^2 A) हम जानते है -[1 + cot^2A = cosec^2A] [cosec^4A = (1 + cot^2A)^2=1 + cot^4A + 2 cot^2A] =cosec^4A – cot^4A – cot^2A – cosec^2A =1 + cot^4A + 2 cot^2A – cot^4A – cot^2A – cosec^2A = 1 + cot^2A – cosec^2A = cosec^2A - cosec^2A = 0 इसलिए सही उत्तर विकल्प A है।

Question

What is the simplified value of (cos A + sin A)(cot A + tan A)?

(Cos A + sin A) (cot A + tan A) का सरलीकृत मान क्या है?

A.sec A + cosec A(sec A + cosec A)

B.sin A + cos A(sin A + cos A)

C.tan A + cot A(tan A + cot A)

D.sec A – cosec A(sec A – cosec A)

Answer

A.(Cos A + Sin A) (cot A + tan A) =(Cos A + Sin A)(Cos A/Sin A+ Sin A/CosA) =(Cos A + Sin A)(Cos^2 A+Sin^2 A / Cos A . Sin A) =(Cos A + Sin A)(1/ Cos A . Sin A) =Cos A/Cos A . Sin A + Sin A/Cos A . Sin A =1/Sin A +1/Cos A =Cosec A + Sec A So the correct answer is option A.

Question

If sin? + cos? = v3 cos(90 - ?), then what is the value of tan??

अगर sinθ + cosθ = √3 cos(90 - θ), तब tanθ का मान क्या है?

A.v3 - 1(√3 - 1)

B.v3 + 1(√3 + 1)

C.(v3 + 1)/2((√3 + 1) /2)

D.(v3 - 1)/2((√3 - 1) /2)

Answer

C.sinθ + cosθ = √3 cos(90 - θ) sinθ + cosθ= √3 sinθ cosθ= √3 sinθ -sinθ cosθ= sinθ(√3 -1) sinθ/cosθ=1/(√3 -1) tanθ=1/(√3 -1) tanθ=1*(√3 +1)/(√3 -1)*(√3 +1) tanθ=(√3 +1)/2 So the correct answer is option C.

C.sinθ + cosθ = √3 cos(90 - θ) sinθ + cosθ= √3 sinθ cosθ= √3 sinθ -sinθ cosθ= sinθ(√3 -1) sinθ/cosθ=1/(√3 -1) tanθ=1/(√3 -1) tanθ=1*(√3 +1)/(√3 -1)*(√3 +1) tanθ=(√3 +1)/2 इसलिए सही उत्तर विकल्प C है।