Math, asked by Shanaya1122, 1 year ago

give me fast answer plz help me to solve it

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Answered by Anonymous
3

1. p^2 = cosec^2θ + cot^2θ + 2cosecθ cotθ

p^2 - 1 = cosec^2θ + cot^2θ + 2cosecθ cotθ - cosec^2θ + cot^2θ

p^2 - 1 = 2cot^2θ + 2cosecθ cotθ

similarly p^2 + 1 = 2cosec^2θ + 2cosecθ cotθ

dividing p^2 - 1 and p^2 + 1 we get cosθ

2. tan^2θ + sec^2θ + 2tanθ secθ = l^2

l^2 + 1 = tan^2θ + sec^2θ + 2tanθ secθ + sec^2θ - tan^2θ

l^2 + 1 = 2sec^2θ + 2tanθ secθ

2l = 2(secθ + tanθ)

dividing l^2 + 1 by 2l we get secθ

3. From the question secθ is positive and if secθ is positive then θ belongs to either 1st quadrant or 4th quadrant.

1st case if θ belongs to 1st quadrant then tanθ is also positive

secθ = x + 1/4x then tanθ = x - 1/4x ( values can be obtained by right angled triangle)

then secθ + tanθ = 2x

2nd case if θ is in 4th quadrant then tanθ is negative.

secθ = x + 1/4x then tanθ = 1/4x - x then secθ + tanθ = 2/4x = 1/2x

  • Identities used to solve 1st and 2nd problem are
  • sec^θ - tan^2θ = 1
  • cosec^2θ - cot^2θ =1


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