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Chapter 5: Trigonometric Functions – Exercise 5.2

Trigonometric Functions – Exercise 5.2 – Q.1

we have,

cosec2θ - cot2θ = 1

⟹ cosec2 θ = 1 + cot2 θ

In the third quadrant cosec θ is negative

Trigonometric Functions – Exercise 5.2 – Q.1

We have,

sin2θ + cos2θ = 1

⟹ sin2θ = 1 - cos2θ 

In the 2nd quadrant sin θ is positive and tan θ is negative

In the third quadrant cosec θ is negative

We have,

sin2θ + cos2 θ = 1

⟹ cos2 θ = 1 - sin2 θ

In the 1st quadrant cos θ is positive and tan θ is also positive

 

Trigonometric Functions – Exercise 5.2 – Q.2

We have,

sin2θ + cos2θ = 1

⟹ cos2θ = 1 - sin2θ

In the 2st quadrant cos θ is negative and tan θ is also negative

Trigonometric Functions – Exercise 5.2 – Q.2

 

Trigonometric Functions – Exercise 5.2 – Q.3

We have,

⟹ θ lies in the second quadrant and Φ lies in the third quadrant.

Now, sin2 θ + cos2 θ = 1

⟹ cos2 θ = 1 - sin2 θ

In the 2st quadrant cos θ is negative and tan θ is also negative

In the third quadrant sec Φ is negative


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