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In this lesson, we will learn how to use addition formulas to simplify trigonometric expressions.

Q1:

Given that c o s π = β β 5 3 , where 0 β€ π β€ π , and c o s π = β 2 3 , where 0 β€ π β€ π , find the exact value of c o s ( π + π ) .

Q2:

Simplify s i n c o s c o s s i n 1 4 7 1 2 0 β 1 4 7 1 2 0 β β β β .

Q3:

Find c o s ( π΄ β π΅ ) given s i n s i n π΄ π΅ = 6 1 3 and c o s c o s π΄ π΅ = 9 2 3 where π΄ and π΅ are acute angles.

Q4:

Find t a n ( π΄ + π΅ ) , given t a n π΄ = β 4 3 where 3 π 2 < π΄ < 2 π and t a n π΅ = 1 5 8 where 0 < π΅ < π 2 .

Q5:

Find c o s ( π΄ + π΅ ) , given s i n s i n π΄ π΅ = 5 2 9 and c o s c o s π΄ π΅ = 1 3 where π΄ and π΅ are acute angles.

Q6:

Given that s i n π΄ = 4 5 , where 0 < π΄ < 9 0 β β and t a n π΅ = 7 2 4 , where 1 8 0 < π΅ < 2 7 0 β β , determine c o s ( π΄ + π΅ ) .

Q7:

Given that s i n π΄ = 4 5 , where 9 0 < π΄ < 1 8 0 β β , and t a n π΅ = 1 2 5 , where 1 8 0 < π΅ < 2 7 0 β β , determine s i n ( π΄ + π΅ ) .

Q8:

Find c o t ( π΄ β π΅ ) given c o s π΄ = 4 5 and s i n π΅ = 7 2 5 where π΄ and π΅ are two positive acute angles.

Q9:

Find s e c ( π΄ β π΅ ) without using a calculator given s e c π΄ = 5 4 and c s c π΅ = 1 3 1 2 where π΄ and π΅ are acute angles.

Q10:

Given that s i n 2 π΄ = 4 4 1 8 4 1 , where 1 8 0 < π΄ < 2 7 0 β β , and t a n π΅ = β 5 1 2 , where 9 0 < π΅ < 1 8 0 β β , find c o t ( π΄ + π΅ ) .

Q11:

Find c o s ( π΄ + π΅ ) given t a n π΄ = 5 1 2 where π < π΄ < 3 π 2 and t a n π΅ = β 4 3 where π 2 < π΅ < π .

Q12:

Find c o t ( π΄ + π΅ ) given s i n π΄ = 5 1 3 and t a n π΅ = 3 4 where π΄ and π΅ are acute angles.

Q13:

Find s i n ( π΄ + π΅ ) given s i n π΄ = β 2 4 2 5 where 2 7 0 β€ π΄ < 3 6 0 β β and c o s π΅ = 4 5 where 0 β€ π΅ < 9 0 β β .

Q14:

Given that s i n π = β 3 2 , where 0 β€ π β€ π 2 , and c o s π = 2 β 2 3 , where 3 π 2 β€ π β€ 2 π , find the exact value of t a n ( π β π ) .

Q15:

Given that c o s π = β 3 5 , where π 2 β€ π β€ π , and s i n π = 1 3 , where π 2 β€ π β€ π , find the exact value of s i n ( π β π ) .

Q16:

Given that c o s π = β 3 4 , where π 2 β€ π β€ π , and c o s π = β β 2 2 , where π β€ π β€ 3 π 2 , find the exact value of t a n ( π + π ) .

Q17:

Given that s i n π = β β 3 3 , where π β€ π β€ 3 π 2 , and s i n π = 1 3 , where π 2 β€ π β€ π , find the exact value of s i n ( π + π ) .

Q18:

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

Q19:

Using the relation t a n t a n t a n t a n t a n ( πΌ + π½ ) = πΌ + π½ 1 β πΌ π½ , find an expression for t a n ( πΌ β π½ ) in terms of t a n πΌ and t a n π½ which holds when ( πΌ β π½ ) β π 2 + π π .

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