Question

prove that. sin80-cos70=cos50

Answer 1

sin80=cos50+cos70
cosC+cosD=2cosC+D/2cosC-D/2
=2cos120/2cos-20/2
2cos60cos(-10)
=2×1/2cos10=cos10=sin(90-10)=sin80

Answer 2

Answer:

Step-by-step explanation:

We have to prove that $sin80^{{\circ}}-cos70^{{\circ}}=cos50^{{\circ}}$

⇒$sin80^{{\circ}}=cos50^{{\circ}}+cos70^{{\circ}}$

Now, using formula, $cos(C+D)= 2cos\frac{C+D}{2}cos\frac{C-D}{2}$

⇒$sin80^{{\circ}}=2 cos\frac{50+70}{2}cos\frac{50-70}{2}$

⇒$sin80^{{\circ}}=2cos60^{{\circ}}cos(-10)^{{\circ}}$

We know that,$cos(-\alpha)=cos\alpha$,therefore,

⇒$sin80^{{\circ}}=2cos60^{{\circ}}cos10^{{\circ}}$

⇒$sin80^{{\circ}}=2{\times}\frac{1}{2}{\times}cos(90^{{\circ}}-80^{{\circ}})$

⇒$sin80^{{\circ}}=sin80^{{\circ}}$

Since, L.H.S=R.H.S, hence proved.