Question

evaluation the following sin^2 42°-sin^2 12°=​

Answer 1

Answer:

sin^(242°)−sin^(212°)

Decimal Form:

0.49878202

Step-by-step explanation:

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Answer 2

Answer:

$sin^2(42)-sin^2(12)=\frac{\sqrt{5}+1 }{8}$

Step-by-step explanation:

using trigonometric identity:

$sin^2 A-sin^2 B=sin(A-B)sin(A+B)$

where, A=42 and B=12

substitute in the formula,

$sin^2(42)-sin^2(12)=sin(42-12)sin(42+12)$

$sin^2(42)-sin^2(12)=sin(30)sin(54)$

$sin^2(42)-sin^2(12)=\frac{1 }{2}$ ×$sin(54)$

we know,$sin(54)=\frac{\sqrt{5}+1 }{4}$

$sin^2(42)-sin^2(12)=\frac{1}{2}$ × $\frac{\sqrt{5}+1 }{4}$

$sin^2(42)-sin^2(12)=\frac{\sqrt{5}+1 }{8}$

therefore, $sin^2(42)-sin^2(12)=\frac{\sqrt{5}+1 }{8}$

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