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In this lesson, we will learn how to use the product-to-sum identity to evaluate a trigonometric expression.

Q1:

Simplify s i n c o s c o s s i n ( π₯ + π¦ ) π¦ β ( π₯ + π¦ ) π¦ .

Q2:

Simplify c o s c o s ( π΄ β π΅ ) β ( π΄ + π΅ ) .

Q3:

Find the value of c o s 3 π , given 5 π + 4 = 0 c o s where 2 π β ] 0 , 2 π [ .

Q4:

Find the value of s i n s i n s i n s i n s i n s i n 2 2 2 2 2 2 π 1 2 + 3 π 1 2 + 5 π 1 2 + 7 π 1 2 + 9 π 1 2 + 1 1 π 1 2 .

Q5:

The intensity of an electric current is given by πΆ = 5 2 ( 7 5 π‘ ) s i n β where π‘ is the time in seconds. Find the intensity after one second without using a calculator using sum and product formulae.

Q6:

Find the exact value of 2 ( 1 9 5 ) ( 4 5 ) c o s s i n .

Q7:

Find, without using a calculator, the value of t a n 2 ( π΅ + π΄ ) given t a n π΄ = 5 7 where π΄ β ο 0 , π 2 ο and t a n π΅ = β 3 7 where π΅ β ο π 2 , π ο .

Q8:

Write the expression s i n s i n ( 8 0 ) + ( 2 0 ) as a product of trigonometric expressions.

Q9:

Find the value of c o s c o s s i n s i n 5 π π + 5 π π given s i n 2 π = 2 1 1 .

Q10:

Find, without using a calculator, the value of t a n ( 2 π΄ + π΅ ) given t a n π΄ = 3 where π΄ β ο 0 , π 2 ο and t a n π΅ = β 7 4 where π΅ β ο π 2 , π ο .

Q11:

Write the expression 4 ( 7 0 ) ( 3 3 ) c o s c o s as a sum or difference of trigonometric expressions.

Q12:

Find the value of s i n s i n s i n s i n s i n s i n s i n s i n 2 2 2 2 2 2 2 2 π 1 6 + 3 π 1 6 + 5 π 1 6 + 7 π 1 6 + 9 π 1 6 + 1 1 π 1 6 + 1 3 π 1 6 + 1 5 π 1 6 .

Q13:

Find c o s ( 2 π + π ) given 1 2 π = 5 t a n and 4 π = 3 t a n where π and π are acute angles.

Q14:

Find the value of t a n ( π΄ β 2 π΅ ) given 2 9 π΄ + 2 1 = 0 c o s where π΄ is the smallest positive angle and 3 π΅ β 4 = 0 t a n where 1 8 0 < π΅ < 2 7 0 β β .

Q15:

Simplify s i n s i n ( π΄ + π΅ ) β ( π΄ β π΅ ) .

Q16:

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

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