Question
If cos (A + 31°) = sin 47°, then what is the value of sin 5A?
यदि cos (A + 31 °) = sin 47 ° है, तो sin 5A का मान क्या है ?
A.
B.
C.
D.
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.
B.
C.
D.
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.
B.
C.
D.
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.
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 इसलिए सही उत्तर विकल्प A है।
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.
B.
C.
D.
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।