Question

prove that 1 + tan^2 ( 45°-A) /
1 - tan^2 (45°-A) = cosec2A​

Answer 1

Answer:

1–tan²(45°–A)/1+tan(45°–A) = cosec2A

On taking L.H.S......

1–tan²(45°–A)/1+tan(45°–A)...........(1)

As we know that.....sec²A = 1+tan²A then from equation (1)

=>1–tan²(45°–A)/sec²(45°–A)

=>1/sec² (45°–A) – tan²(45–A)/sec²(45–A)

=>cos²(45–A) – sin²(45–A)

{ Because cosA = 1/secA and tanA/secA = sinA}

=>cos2(45°–A)

{ Because 1 – cos²A = sin2A }

=>sin(90°–2A)

=>cosec2A { Because sin(90–A) = cosecA }

= R.H.S.

HOPE IT HELPS.....

PLZZ MARK AS BRAINLIEST