Question

if tan alpha = 1 then find cot alpha, sin alpha and sec alpha
pls answer....in a bit details
thank you in advance​

Answer 1

Given : tan α = 1

To find : sin α, sec α and cot α

Solution :

=> tan α = 1

Squaring both sides,

=> tan²α = 1

Apply formula :

• sec² α -1 = tan² α

=> sec²α -1 = 1

=> sec²α = 2

=> sec α =√2

=> sec α = 1/cos α

=> cos α = 1/√2

Squaring both sides

=> cos²α = 1/2

Apply formula :

• cos²α = 1- sin²α

=> 1 - sin²α = 1/2

=> 1-1/2 = sin²α

=> 1/2 = sin² α

=> √1/2 = sin α

=> 1/√2 = sin α

cosec α = 1/ sin α = √2

We know that, cot α = cosec α / sec α

=> cot α = √2 / √2

=> cot α = 1

Required answers :-

• cot α = 1

• sin α = 1/√2

• sec α = √2

More formulas :-

• sin² A + cos² A = 1

• sec² A - tan² A = 1

• 1 + cot² A = cosec² A

• sin A = 1/ cosec A

• cosec A = 1/ sin A

• sec A = 1/ cos A

• cos A = 1/ sec A

• tan A = 1/ cot A

• cot A = 1/ tan A