1. derive this identity from the sum and difference formulas for cosine:

sin a sin b = (1 / 2)[cos(a – b) – cos(a + b)]

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2. use the trigonometric subtraction formula for sine to verify this identity:

sin((π / 2) – x) = cos x

calculation:

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My math teacher told my class to "steal" a 6th grade fraction word problem from the internet, word problems? : -p requirements: only a 1 step word problem. needs to be complex.

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality

Currently, the largest cruise ship has a tonnage of 225,282 gross tons (gt). which of the following is a reasonable estimate for the tonnage of this cruise ship? a. 2 × 10^5 gt b. 2 × 10^6 gt c. 2 × 10^-5 gt d. 2 × 10^-6 gt