Q. 13

# If secθ = 5/4, show that

We have, secθ = 5/4 = 1/cosθ

cosθ = (4k)/(5k) = AC/AB (For some value of k)

By Pythagoras theorem, (hypotenuse)2 = (perpendicular)2 + (base)2

AB2 = BC2 + AC2

= (5k)2 = BC2 + (4k)2

= 25k2 = BC2 + 16k2

= BC2 = 9k2

BC = 3k

sinθ = BC/AB = (3k)/(5k) = 3/5

consider the LHS

LHS = =

=

=

=

=

= 12/7

= RHS

HENCE PROVED

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