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Given that cos z = L , whrere z is an acute angle, find an e...

Given that cos z = L , whrere z is an acute angle, find an expression for cotzcsczsecz+tanz

A.

1L1+L

B.

L231+L

C.

1+L3L2

D.

L(L1)1L+11L2

Correct answer is D

Given Cos z = L, z is an acute angle

cot z - cosec zsec z + tan z = cos z

= cos zsin z

cosec z = 1sin z

cot z - cosec z = cos zsin z - 1sin z

cot z - cosec z = L1sin z

sec z = 1cos z

tan z = sin zcos z

sec z = 1cos z + sin zcos z

= 1l + sin zL

the original eqn. becomes

cot z - cosec zsec z + tan z = L1sin z1+sinzL

= L(L1)sin z(1+sin z)

= L(L1)sin z+1cos2z

= sin z + 1

= 1 + 1L2

= L(L1)1L+11L2