Question

If 3tan a is equal to 4 then find sin a and cos a

Answer 1

Given that 3tan∅=4

Now,

tan∅ = 4/3...........[1]

We know that,

sec²∅ - tan²∅ = 1

→sec²∅ = 1 + tan²∅

→sec²∅ = 1 + 16/9 [From [1]]

→sec²∅=25/9

→sec∅=5/3

We know that,

cos∅=1/sec∅

→cos∅=1/(5/3)

→cos∅=3/5

From sin²∅ + cos²∅=1,

sin²∅ = 1 - cos²∅

→sin²∅ = 1 -(4/5)²

→sin²∅ = 16/25

→sin∅ = 4/5

Answer 2

$\mathfrak{\underline{\underline{Solution :}}}$

Given that 3tan∅=4

Now,

tan∅ = 4/3...........(1)

We know that,

sec²∅ - tan²∅ = 1

→sec²∅ = 1 + tan²∅

→sec²∅ = 1 + 16/9 From (1)

→sec²∅=25/9

→sec∅=5/3

We know that,

cos∅=1/sec∅

→cos∅=1/(5/3)

→cos∅=3/5

From sin²∅ + cos²∅=1,

sin²∅ = 1 - cos²∅

→sin²∅ = 1 -(4/5)²

→sin²∅ = 16/25

→sin∅ = 4/5

"Take ∅ as theta"