Using sum and difference identities, establish the reductions formula.
cot⁡〖(-7π/2- φ)=tanφ〗
sin⁡〖(3π/2- x)= -cos⁡x 〗

Prove the following identities.
⁡csc⁡x/sec⁡x ⁡〖=(1+cot⁡x)/(1+tan⁡x )〗
(sin⁡〖1/2 x-cos⁡〖1/2 x)²=1-sin⁡x 〗〗

Find the exact value.
sin⁡〖50°cos⁡〖40°+〖sin 〗⁡〖40°cos⁡〖50°〗〗〗〗
tan⁡〖π/3+tan⁡〖π/6〗〗/(1-tan⁡〖π/3 tanπ/6〗 )

Question

Using sum and difference identities, establish the reductions formula.
	cot⁡〖(-7π/2- φ)=tanφ〗
	sin⁡〖(3π/2- x)= -cos⁡x 〗

Prove the following identities.
	⁡csc⁡x/sec⁡x ⁡〖=(1+cot⁡x)/(1+tan⁡x )〗 
	(sin⁡〖1/2 x-cos⁡〖1/2 x)²=1-sin⁡x 〗 〗

Find the exact value.
	sin⁡〖50°cos⁡〖40°+〖sin 〗⁡〖40°cos⁡〖50°〗 〗 〗 〗
	 tan⁡〖π/3+tan⁡〖π/6〗 〗/(1-tan⁡〖π/3  tanπ/6〗 )