Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to simplify trigonometric expressions by applying trigonometric identities.

Q1:

Simplify ( 1 β π ) + ( 1 + π ) t a n t a n 2 2 .

Q2:

Simplify s i n c o s c s c c o t 2 2 2 2 π + π π β π .

Q3:

Simplify 1 β π π β π s i n c s c c o t 2 2 2 .

Q4:

Simplify s e c s e c t a n 2 2 2 π β 1 π β π .

Q5:

Find the value of t a n c o t ( π + π΄ ) β ο» π΄ β π 2 ο given 2 1 π΄ = β 2 9 c s c where 3 π 2 < π΄ < 2 π .

Q6:

Find the possible values of t a n c o t 2 2 π β π given that t a n c o t π + π = 2 4 .

Q7:

Knowing that 5 + 4 π₯ = β 1 2 π₯ c o s t a n 2 , find t a n π₯ .

Q8:

Find the set of values satisfying s e c t a n t a n 2 2 π β π + β 3 π = 0 where 0 β€ π < 3 6 0 β β .

Q9:

Find the set of values satisfying s e c t a n t a n 2 2 π β π β π = 0 where 0 β€ π < 3 6 0 β β .

Q10:

Find the set of values satisfying s e c t a n t a n 2 2 π β π β β 3 π = 0 where 0 β€ π < 3 6 0 β β .

Q11:

Find the set of values satisfying β 3 π β β 3 π + π = 0 s e c t a n t a n 2 2 where 0 β€ π < 3 6 0 β β .

Q12:

Simplify 1 + π c o t 2 .

Q13:

Simplify s e c t a n 2 2 π β π .

Q14:

Simplify t a n 2 π + 1 .

Q15:

Simplify c o t s i n c o s 2 2 2 π + π + π .

Q16:

Simplify s e c s i n c o s 2 2 2 π β π + π .

Q17:

Simplify 1 + π 1 + π t a n c o t 2 2 .

Q18:

Simplify 1 + ( 9 0 β π ) c o t 2 β .

Q19:

Suppose that 1 7 πΌ β 8 = 0 s i n with 0 < πΌ < 9 0 β β , and that π½ is the largest angle between 0 β and 3 6 0 β for which 3 π½ + 4 = 0 t a n . Find the exact value of c s c c o t s e c t a n ( 1 8 0 + πΌ ) ( 9 0 β π½ ) β ( 3 6 0 + πΌ ) ( 3 6 0 β π½ ) β β β β .

Q20:

Find the value of t a n c o t 3 3 π + π given t a n c o t π + π = 1 6 .

Q21:

π΄ π΅ πΆ is a triangle where t a n π΄ = 1 4 and π΅ = 2 π΄ . Find s i n πΆ without using a calculator.

Q22:

Simplify ( 1 + π ) β 2 π c o t c o t 2 .

Q23:

Simplify 1 + ο» β π ο 1 + ο» β π ο c o t t a n 2 3 π 2 2 π 2 .

Donβt have an account? Sign Up