Question

If A+B= 90° then show that 1+ cot squar A = sec square B

Answer 1

A + B= 90

==> A = B-90

1 + cot²A
= cosec²A (using identity cosec²A - cot²A = 1)
= cosec² (90-B)
= sec²B (using identity cosec(90-A) = secA)

Hence proved. :-)

Answer 2

Given,

A+B=90→B=90-A

To prove that,

1+cot²A=sec²B

We know that,

cosec²A-cot²A=1

→cosec²A=1+cot²A.............[1]

Also,

cosecA=sec(90-A)

→cosecA=secB..................[2]

Using [2] in [1],

1+cot²A=sec²B

Hence,proved

•Some basic trigonometric identities,

sin²x+cos²x=1

sec²x-tan²x=1

cosec²x-cot²x=1

•Trigonometric relations:

sin x=cos(90-x)

tan x=cot(90-x)

sec x=cosec(90-x)

•Trignometric functions:

sin x=1/cosec x

cos x=1/sec x

tan x=1/cot x