Question

If cos A=2/5,find the value of 4+4tan²A

Answer 1

answer is 25

4+4tan2=4(1+tan2)

=4(sec2)

=4×1/cos2

=4×(5/2)2

=25

Answer 2

Question :

If cos A=2/5,find the value of 4+4tan²A

ANSWER :

We have to find the value of

4+4tan²A

by taking 4 common

= 4(1+tan²A)

but 1+tan²A=sec²A is a trigonometric identity

we get

4(1+tan²A)

= 4sec²A

but sec²A = 1/cos²A

so 4 sec²A

= 4 / cos²A

now as it is given that cosA = 2/5

the expression becomes

4/cos²A

= 4/(2/5)²

= 4/(4/25)

= (4×25)/4

=25

NOTE :

while solving such questions

you must first simplify the expression

and when the expression arrives in the form which we had given

we can put the value and get the answer