Given tan theta =9, use trigonometric identities to find the exact value of each of the following: a) sec sqr Theta
b) Cot theta
c) cot (pie/2-Theta)
d) csc sqr theta

Step-by-step explanation:

Given

Required

Solve (a) to (d)

Using tan formula, we have:

This gives:

Rewrite as:

Using a unit ratio;

Using Pythagoras theorem, we have:

Take square roots of both sides

So, we have:

Solving (a):

This is calculated as:

Where:

So:

Solving (b):

This is calculated as:

Where:

---- given

So:

Solving (c):

In trigonometry:

Hence:

Solving (d):

This is calculated as:

Where:

So:

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step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it