IIT JEE , AIEEE Forum - Mathematics , Trignometry

m.viddya

Q.The no. of roots of the eq sec²

+cosec²

= 8 in [0,

] is?

1.1

2.2

3.6

4.4

Greatdreams

You have sin ² x + cos ² x = 8 sin ² x cos ² x

so 1/8 = sin ² x cos ² x

1/2 = 4sin ² x cos ² x

So (sin 2x)²= 1/ 2

or Sin 2x = + -1/

2

Now if we plot the graph we get 4 values for 0 to

So answer is 4

edited....

anchitsaini

ans seems to be 4

anchitsaini

sorry it is 2 only

anchitsaini

no now i think it is 4 only
by the method greatdreams used only-sin2x=+-1/underroot 2
and not only positive value hence we will get four values on drawing the graph

anchitsaini

well i can explain the graph of sin2x.
this graph would have the same range but domain would be half that of sinx that is 2pie/2=pie hence the graph of sinx is the graph of sin2x only but within 0-pie

m.viddya

Can som1 plz explain why we get 4 values on da graph?

m.viddya

thx...

akhil_o

See drawing possible values for sin 2x=+-1/rt 2

and then dividing angles by 2 we have all values

all the intersections(in blue) refer to required solns in 0, pi

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