Question

show that sin15 degree/cos75degree=1​

Answer 1

Answer:

sin 15° ÷ cos 75° = 1

Step-by-step explanation:

Concept used:

Here we apply the concept of complimentary angles. Some important identities are:

• sin (90 - x) = cos x
• cos (90 - x) = sin x
• tan (90 - x) = cot x

Solution:

Applying the first identity from above,

sin 15° can be written as sin (90° - 75°)

This is equal to cos 75°

We just derived that sin 15° = cos 75°

Replace sin 15° by cos 75° in the question.

So, we get;

cos 75°/cos 75°

= 1

★ HENCE PROVED ★

Extra information:

While drawing the graph of trigonometric functions,

• All functions are positive in First Quadrant
• Sin and Cosec are positive and others are negative in second Quadrant
• Tan and Cot are positive and others are negative in third Quadrant.
• Cos and sec are positive and others are negative in forth Quadrant.