Question

prove that tan theta is equal to sin theta by cos theta​

Answer 1

Answer:

1st Method :

sin∅/cos∅=tan∅

Take ∅=0

sin 0/cos0

=0/1

=0=LHS

tan 0

=0=LHS

Hence proved

2nd method:

Draw a right-angled triangle ABC. Name AB as the base or adjacent, CB as the altitude or opposite, AB as hypotenuse and right angle at C.

sin A = BC/AB and cos A = AC/AB

Divide sin A by cos A = BC/AB/[AC/AB] = [BC/AB]*[AB/AC] = BC/AC = (altitude or opposite)/(base or adjacent)

tan A = (altitude or opposite)/(base or adjacent), same as BC/AC which is

sin A /cos A.Hence tan A = sin A /cos A. ProvedDraw a right-angled triangle ABC. Name AB as the base or adjacent, CB as the altitude or opposite, AB as hypotenuse and right angle at C.

sin A = BC/AB and cos A = AC/AB

Divide sin A by cos A = BC/AB/[AC/AB] = [BC/AB]*[AB/AC] = BC/AC = (altitude or opposite)/(base or adjacent)

tan A = (altitude or opposite)/(base or adjacent), same as BC/AC which is

sin A /cos A.

Hence tan A = sin A /cos A. Proved

Answer 2

Step-by-step explanation:

generally , this formula but we prove like this.

tan (alpa )= sin(alpa)/cos(alpa)

we can take triangle ABC