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Without using tables, evaluate the following: (sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°). - Mathematics

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Question

Without using tables, evaluate the following: (sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°).

Sum
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Solution

(sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°).

sin30° = `(1)/(2)`

sin45° = `(1)/sqrt(2)`
sin90° = 1

cos45° = `(1)/sqrt(2)`

cos60° = `(1)/(2)`
(sin90° + sin45° + sin30°)(sin90° - cos45° + cos60°)

= `(1 + 1/sqrt(2) + 1/sqrt(2))(1 - 1/sqrt(2) + 1/sqrt(2))`

= `(3/2 + 1/sqrt(2))(3/2 - 1/sqrt(2))`

= `(3/2)^2 - (1/sqrt(2))^2`

= `(9)/(4) - (1)/(2)`

= `(9 - 2)/(4)`

= `(7)/(4)`.

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Chapter 27: Trigonometrical Ratios of Standard Angles - Exercise 27.1

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Frank Mathematics [English] Class 9 ICSE
Chapter 27 Trigonometrical Ratios of Standard Angles
Exercise 27.1 | Q 1.09
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