Question

verify sin theta-cos theta+1/sin theta +cos theta-1=1/sec theta-tan theta.​

Answer 1

Answer:

LHS = (sinθ - cosθ + 1)/(sinθ + cosθ - 1)

dividing by cosθ both Num and den

= (sinθ/cosθ - cosθ/cosθ + 1/cosθ)/(sinθ/cosθ + cosθ/cosθ - 1/cosθ)

= (tanθ + secθ - 1)/(tanθ - secθ + 1)

MultiplyIing (tanθ - secθ) with both Num and den

= (tanθ + secθ - 1)(tanθ - secθ)/(tanθ - secθ + 1)(tanθ - secθ)

= {(tan²θ - sec²θ) - (tanθ - secθ)}/(tanθ - secθ + 1)(tanθ - secθ)

= (-1 - tanθ + secθ)/(tanθ - secθ + 1)(tanθ - secθ)

[ ∵ sec²x - tan²x = 1 ]

= -1/(tanθ - secθ)

= 1/(secθ - tanθ)

= RHS

Step-by-step explanation:

Answer 2

Answer:

Your answer attached in the photo

replace theta by A