Question

Sin21 cos9-cos84 cos6

Answer 1

Answer:

tan90.585674 by cambridge method

Answer 2

The value of sin21°cos9°-cos84°cos6° is   $\frac{1}{4}$.

Given:

sin21°cos9°-cos84°cos6°

To Find:

The value of sin21°cos9°-cos84°cos6°

Solution:

sin21°cos9°-cos84°cos6°

= sin21°cos9°-cos(90°-6°)cos6°

= sin21°cos9°-sin6°cos6°

Multiplying and dividing by 2

= $\frac{1}{2}$ (2sin21°cos9°-2sin6°cos6°)

Formula:

2sinAcosB= sin(A+B)+sin(A-B) here, A=21° and B= 9°

2Sinθcosθ= sin(2θ) here, θ= 6

=  $\frac{1}{2}$ (sin(21°+9°)+sin(21°-9°)-sin(2×6°))

= $\frac{1}{2}$ (sin30°+sin12°-sin12°)

= $\frac{1}{2}$ (sin30°)

=  $\frac{1}{2}$ × $\frac{1}{2}$

=  $\frac{1}{4}$

Therefore, The value of sin21°cos9°-cos84°cos6° is   $\frac{1}{4}$.

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