Question

if a + b is equal to 90 degree show that 1 + cot square a is equal to sec square b

Answer 1

a+b=90
b=90-a..............(1)

1+cot²a=sec²b
LHS

⇒1+cot²a
⇒cosec²a             (1+cot²Ф=cosec²Ф)
⇒cosec²(90-a)

from (1)

⇒sec²(b)
⇒sec²b
                                  HENCE PROVED

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