Question

Tan theta = 1/√5 , find the value of (cosec^2 theta - sec^2 theta) / (cosec^2 theta + sec^2 theta)

Answer 1

It has given that tanθ = 1/√5

To find : The value of (cosec²θ - sec²θ)/(cosec²θ + sec²θ)

solution : here tanθ = 1/√5 = p/b

so, p = 1 and b = √5

from Pythagoras theorem, h = √(1² + √5²) = √6

now cosecθ = h/p = √6/1 = √6

secθ = h/b = √6/√5

now (cosec²θ - sec²θ)/(cosec²θ + sec²θ)

= {(√6)² - (√6/√5)²}/{(√6)² + (√6/√5)²}

= (6 - 6/5)/(6 + 6/5)

= (30 - 6)/(30 + 6)

= 24/36

= 2/3

Therefore the value of (cosec²θ - sec²θ)/(cosec²θ + sec²θ) is 2/3

Answer 2

Answer:

2/3

Step-by-step explanation:

Here AB=1,BC=root5 and AC=root6

tantheeta=1/root5

cosectheeta=root6

sectheeta=root6/root5

=(cosec^2theeta-sec^2theeta)÷(cosec^2theeta+sec^2theeta)

=(root6)^2-(root6/root5)^2÷(root6)^2+(root6/root5)^2

=6-6/5÷6+6/5

=30-6÷30+6

=24÷36

=2/3 is answer