The value of 1+cos56°+cos58°-cos66°is
4cos28°cos29°sin33°
cos28°cos29°sin33°
4cos28°sin29°cos33°
4cos28°sin29°sin33°
Explanation for the correct option.
Find the value.
Given: 1+cos56°+cos58°-cos66°
Formula used 1-cos2A=2sin2A,cosA+cosB=2cosA+B2cosA-B2
⇒1-cos66°+cos58°+cos56°=2sin233°+2cos58°+56°2cos58°-56°2=2sin233°+2cos57°cos1°=2sin233°+2cos(90-33)°cos(90-89)°=2sin233+2sin33°sin89°=2sin33°(sin33°+sin89°)=2sin33°(2sin61°cos28°)sinA+sinB=2sinA+B2cosA-B2=2sin33°2sin(90-29)°cos28°=2sin33°×2cos29°cos28°=4sin33°cos29°cos28°
Hence option(A) is the correct answer.
1+cos 56∘+cos 58∘−cos 66∘=