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[CIE] All Pure Mathematics (P1, P2 and P3) doubts here !

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sameer210394:
Let 'a' and 'b' be the straight lines with equations y=m1x+c1 and y=m2x+c2 where m1m2 not equal to zero. Use appropriate trigonometric formulae to prove that 'a' and 'b' are perpendicular if and only if m1m2 = -1.

astarmathsandphysics:
The trig formulae is tan
m1=tan theta 1 and m2=tan theta 2
Two lines are perprendicular is theta 2 = theta 1 +90
tan theta 2 = tan (theta 1 +90) =- 1/(tan theta 1)
so m1 m2 =tan theta 1 tan theta 2 =-1

Mrsmart1017:
Help pleazzz

sameer210394:
Use the inequality sinx < x < tanx for a suitable value of x to show that Pi lies between 3 and 2(root3)

sameer210394:
p/q = root3

(cosx + sinx) / (cosx - sinx) = root3

divide numerator & denominator by cosx

(1 + tanx) / (1 - tanx) = root3

tanx = (root3 -1) / (root3 +1)

x = 15, 195

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