Question

Prove that (sec A+ tan A ) ( 1- sin A)=cos A

Answer 1

(ꜱᴇᴄ ᴀ+ᴛᴀɴ ᴀ)(1-ꜱɪɴᴀ)

=(1/ᴄᴏꜱ ᴀ + ꜱɪɴ ᴀ/ᴄᴏꜱ ᴀ)(1-ꜱɪɴᴀ)

=[(1+ꜱɪɴᴀ)/ᴄᴏꜱᴀ](1-ꜱɪɴᴀ)

=(1+ꜱɪɴᴀ)(1-ꜱɪɴᴀ)/ᴄᴏꜱᴀ

=(1-ꜱɪɴ^2 ᴀ)/ᴄᴏꜱᴀ

=(ᴄᴏꜱ^2 ᴀ)/ᴄᴏꜱ ᴀ

=ᴄᴏꜱ ᴀ

Answer 2

Answer:

(sec A+tan A)(1-sinA)

=(1/cos A + sin A/cos A)(1-sinA)

=[(1+sinA)/cosA](1-sinA)

=(1+sinA)(1-sinA)/cosA

=(1-sin^2 A)/cosA

=(cos^2 A)/cos A

=cos A

Hence proved

... plz make it brain list