give me fast answer plz help me to solve it
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Answers
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