Question

prove that:-sin 63degree cos 27degree +cos 63degree sin 27degree =1​

Answer 1

$\huge{\textbf{SOLUTION-}}$

As we know,

$\boxed{sin(90-\theta)\:= cos\theta}$ and,

$\boxed{cos(90-\theta)\:=sin\theta}$

Using this, we get

⇒ sin63°cos27° + cos63°sin27°

⇒sin63°cos(90-63°) + cos63°sin(90-63°)

⇒sin63°sin63° + cos63°cos63°

⇒sin²63° + cos²63°

As we know,

sin²Ф + cos²Ф = 1

Using this, we get

sin²63 + cos²63 = 1

Hence Proved

ADDITIONAL FORMULAE

${1+tan^{2}\theta=sec^{2}\theta}$

${1+cot^{2}\theta=cosec^{2}\theta}$