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Let's prove that when two straight lines meet, then they are perpendicular to each other and if the gradient of one is m then the other is -1/m. So, their product is -1.

From the diagram,
/AB/ and /CD/ meets at E
Also, F meets E from the x - axis
Clearly, a + b = 90° then a + @ = 90
So, b=@ ........ *
Now, the gradient of AB= FE/GF = tan@ (say m)
Again, gradient of CD = - FE/FH = -1/tanb
recall from * that b = @
So, tanb = tan@ = m
Then the gradient of CD = -1/m

The product of the gradients are m • (-1/m) = -1.

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Emmatex Tutorial Centre (EMC)

QUESTION
Prove that sin17°=2sin17/2cos17/2

SOLUTION
We know,
sin(A+A)=sinAcosA+sinAcosA=2sinAcosA

Then,
sin(A/2+A/2)=2sinA/2cosA/2 ......... i

Now,for sin17°
sin17°=sin(17/2+17/2)
Now put A=A/2 in eqn i

We have
sin(17/2+17/2)=2sin17/2cos17/2
=sin17°=2sin17/2cos17/2
Thus,proved

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