Question

if tan thita = 1, then find the value of sin thita + cos thita ÷ sec thita + cosec thita​

Answer 1

Answer:

1/2

Step-by-step explanation:

Given---> tanθ = 1

To find --->

( Sinθ + Cosθ ) / ( Secθ + Cosecθ )

Solution---> ATQ,

tanθ = 1

=> tanθ = tan 45°

=> θ = 45°

Now first we find value of numerator.

Sinθ + Cosθ = Sin45° + Cos45°

= ( 1 / √2 ) + ( 1 / √2 )

= ( 1 + 1 ) / √2

= 2 /√2

= √2

Secθ + Cosecθ = Sec45° + Cosec45°

= √2 + √2

= 2 √2

Now,

( Sinθ + Cosθ ) / ( Secθ + Cosecθ )

= √2 / 2√2

= 1 / 2