Question

sin theta -cos theta+1​

Answer 1

Question

Prove (sin∅ - cos∅ + 1)/(sin∅ + cos∅ - 1) = 1/(sec∅ - tan∅).

Solution

By dividing L.H.S from cos∅

→ {(sin∅ - cos∅ + 1)/cos∅}/{(sin∅ + cos∅ - 1)/cos∅}

→ (sin∅/cos∅ - cos∅/cos∅ + 1/cos∅)/(sin∅/cos∅ + cos∅/cos∅ - 1/cos∅)

→ (tan∅ - 1 + sec∅)/(tan∅ + 1 - sec∅)

Since 1 = sec²∅ - tan²∅

→ (tan∅ + sec∅ - 1)/(tan∅ - sec∅ + sec²∅ - tan²∅)

→ (tan∅ + sec∅ - 1)/{tan∅ - sec∅ + (sec∅ - tan∅)(sec∅ + tan∅)}

→ (tan∅ + sec∅ - 1)/{tan∅ - sec∅ - (tan∅ - sec∅)(sec∅ + tan∅)

→ (tan∅ + sec∅ - 1)/(1 - sec∅ - tan∅)(tan∅ - sec∅)

→ (tan∅ + sec∅ - 1)/(tan∅ + sec∅ - 1)(sec∅ - tan∅)

→ 1/(sec∅ - tan∅) = R.H.S

Hence Proved

Answer 2

ɦεყ ɱαƭε !!

Answer refers to the attachment.

hope it helps..